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600 (number)
600 (number)
600 (number)
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← 599 600 601 →
Cardinalsix hundred
Ordinal600th
(six hundredth)
Factorization23 × 3 × 52
Divisors1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600
Greek numeralΧ´
Roman numeralDC, dc
Binary10010110002
Ternary2110203
Senary24406
Octal11308
Duodecimal42012
Hexadecimal25816
ArmenianՈ
Hebrewת"ר / ם
Babylonian cuneiform𒌋
Egyptian hieroglyph𓍧

600 (six hundred) is the natural number following 599 and preceding 601.

Mathematical properties

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Six hundred is a composite number, an abundant number, a pronic number,[1] a Harshad number and a largely composite number.[2]

Credit and cars

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  • In the United States, a credit score of 600 or below is considered poor, limiting available credit at a normal interest rate
  • NASCAR runs 600 advertised miles in the Coca-Cola 600, its longest race
  • The Fiat 600 is a car, the SEAT 600 its Spanish version

Integers from 601 to 699

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600s

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610s

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620s

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  • 620 = 22 × 5 × 31, sum of four consecutive primes (149 + 151 + 157 + 163), sum of eight consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97), the sum of the first 620 primes is itself prime[15]
  • 621 = 33 × 23, Harshad number, the discriminant of a totally real cubic field[16]
  • 622 = 2 × 311, nontotient, Fine number, (sequence A000957 in the OEIS), it is also the standard diameter of modern road bicycle wheels (622 mm, from hook bead to hook bead)
  • 623 = 7 × 89, number of partitions of 23 into an even number of parts[17]
  • 624 = 24 × 3 × 13 = J4(5),[18] sum of a twin prime pair (311 + 313), Harshad number, Zuckerman number
  • 625 = 252 = 54, sum of seven consecutive primes (73 + 79 + 83 + 89 + 97 + 101 + 103), centered octagonal number,[19] 1-automorphic number, Friedman number since 625 = 56−2,[20] one of the two three-digit numbers when squared or raised to a higher power that end in the same three digits, the other being 376
  • 626 = 2 × 313, nontotient, 2-Knödel number, Stitch's experiment number
  • 627 = 3 × 11 × 19, sphenic number, number of integer partitions of 20,[21] Smith number[22]
  • 628 = 22 × 157, nontotient, totient sum for first 45 integers
  • 629 = 17 × 37, highly cototient number,[23] Harshad number, number of diagonals in a 37-gon[24]

630s

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640s

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650s

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660s

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670s

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680s

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  • 680 = 23 × 5 × 17, tetrahedral number,[61] nontotient
  • 681 = 3 × 227, centered pentagonal number[3]
  • 682 = 2 × 11 × 31, sphenic number, sum of four consecutive primes (163 + 167 + 173 + 179), sum of ten consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89), number of moves to solve the Norwegian puzzle strikketoy[62]
  • 683 = prime number, Sophie Germain prime,[37] sum of five consecutive primes (127 + 131 + 137 + 139 + 149), Chen prime, Eisenstein prime with no imaginary part, Wagstaff prime[63]
  • 684 = 22 × 32 × 19, Harshad number, number of graphical forest partitions of 32[64]
  • 685 = 5 × 137, centered square number[65]
  • 686 = 2 × 73, nontotient, number of multigraphs on infinite set of nodes with 7 edges[66]
  • 687 = 3 × 229, 687 days to orbit the Sun (Mars) D-number[67]
  • 688 = 24 × 43, Friedman number since 688 = 8 × 86,[20] 2-automorphic number[68]
  • 689 = 13 × 53, sum of three consecutive primes (227 + 229 + 233), sum of seven consecutive primes (83 + 89 + 97 + 101 + 103 + 107 + 109). Strobogrammatic number[69]

690s

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  • 690 = 2 × 3 × 5 × 23, sum of six consecutive primes (103 + 107 + 109 + 113 + 127 + 131), sparsely totient number,[27] Smith number,[22] Harshad number
    • ISO 690 is the ISO's standard for bibliographic references
  • 691 = prime number, (negative) numerator of the Bernoulli number B12 = -691/2730. Ramanujan's tau function τ and the divisor function σ11 are related by the remarkable congruence τ(n) ≡ σ11(n) (mod 691).
    • In number theory, 691 is a "marker" (similar to the radioactive markers in biology): whenever it appears in a computation, one can be sure that Bernoulli numbers are involved.
  • 692 = 22 × 173, number of partitions of 48 into powers of 2[70]
  • 693 = 32 × 7 × 11, triangular matchstick number,[71] the number of sections in Ludwig Wittgenstein's Philosophical Investigations.
  • 694 = 2 × 347, centered triangular number,[29] nontotient, smallest pandigital number in base 5.[72]
  • 695 = 5 × 139, 695!! + 2 is prime.[73]
  • 696 = 23 × 3 × 29, sum of a twin prime (347 + 349), sum of eight consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101 + 103), totient sum for first 47 integers, trails of length 9 on honeycomb lattice[74]
  • 697 = 17 × 41, cake number; the number of sides of Colorado[75]
  • 698 = 2 × 349, nontotient, sum of squares of two primes[76]
  • 699 = 3 × 233, D-number[67]

References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

600 (number)

View on Grokipedia
from Grokipedia
600 (six hundred) is the natural number following 599 and preceding 601. It is an even expressible as 23×3×522^3 \times 3 \times 5^2. In , 600 has 24 positive divisors, with their sum equaling 1860, making the sum of its proper divisors 1260, which exceeds 600 and classifies it as an . Additionally, it is a as the product of two consecutive integers, 24 and 25; a since it is divisible by the sum of its digits (6); and a (also known as a Hamming number), being the product of powers of 2, 3, and 5. The number 600 holds significance in higher-dimensional geometry as the , one of the six regular 4-polytopes (or polychora), which consists of 600 regular tetrahedral cells meeting five around each edge. Its dual is the , and together they represent the highest symmetry in four-dimensional space among convex regular polytopes. Euler's totient function value for 600 is 160, indicating the count of integers up to 600 that are coprime to it.

Numerical Properties

Factorization and Divisors

The prime of 600 is 23×31×522^3 \times 3^1 \times 5^2. This decomposition arises by repeatedly dividing 600 by the smallest prime factors: 600 ÷ 2 = 300, 300 ÷ 2 = 150, 150 ÷ 2 = 75, 75 ÷ 3 = 25, 25 ÷ 5 = 5, and 5 ÷ 5 = 1. From the prime , the total number of positive divisors of 600 is calculated using the formula for the , which multiplies one plus each of the exponents in the prime : (3+1)×(1+1)×(2+1)=4×2×3=24(3+1) \times (1+1) \times (2+1) = 4 \times 2 \times 3 = 24. The complete list of these positive divisors is: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, , 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, , . The sum of the divisors of 600, denoted σ(600), is 1860, obtained by adding all 24 divisors or using the multiplicative formula (1+2+22+23)(1+3)(1+5+52)=15×4×31=1860(1 + 2 + 2^2 + 2^3)(1 + 3)(1 + 5 + 5^2) = 15 \times 4 \times 31 = 1860.

Classifications and Representations

600 is a , as it can be expressed as the product of two or more positive integers greater than 1. It is also an , with the sum of its proper divisors equaling 1260, which surpasses 600 itself. Furthermore, 600 qualifies as a , being the product of two consecutive integers: 600=24×25600 = 24 \times 25. In addition, it is a , divisible by the sum of its base-10 digits (6 + 0 + 0 = 6), yielding an integer quotient of 100. Additionally, 600 is a Hamming number (or ), as it can be expressed as a product of powers of 2, 3, and 5. 600 is classified as a largely , possessing 24 positive divisors—a count that is at least as high as that of any smaller positive . It is likewise a refactorable number (or tau number), where the total count of its divisors divides 600, namely 24 divides 600. In , 600 is denoted as DC. Its binary representation is 100101100021001011000_2. In base 10, 600 is an even number and a multiple of 100, aspects that underscore its structural compositeness.

Significance in Culture and Applications

Finance and Credit Scoring

In credit scoring systems, particularly those used in the United States, a FICO score of 600 is classified as "fair," though scores of 600 or below are often indicative of subprime , which can significantly restrict access to favorable lending terms as of 2025 standards. Lenders often view scores in this range as high-risk, leading to limited approvals, denials for conventional mortgages or auto financing, and substantially higher rates for those who do qualify, sometimes 5-10 points above prime rates. This threshold reflects longstanding industry practices where subprime borrowers face elevated costs to compensate for perceived default risks. VantageScore, an alternative model developed by the three major bureaus, categorizes scores from 501 to 600 within its "poor" range under the VantageScore 4.0 framework, signaling similar high-risk profiles and comparable barriers to access. Borrowers at this level may encounter rejections for unsecured personal loans or cards with competitive rewards, though some subprime lenders offer specialized products at premium rates. The average U.S. score stood at approximately 715 in 2024 and remained stable around this level into 2025, highlighting that a score positions individuals well below the national norm and in the bottom of creditworthiness. Introduced by in 1989, the FICO model established the 300-850 scale, with the 600 cutoff for poor/subprime classifications emerging consistently by the early amid post-recession lending reforms. Despite updates like FICO Score 10 in 2020, which refined factors such as payment trends without altering core range boundaries, the 600 threshold has endured as a key benchmark for .

Automotive Models

The , introduced in 1955, was a compact rear-engine designed to provide affordable personal transportation in post-World War II , featuring a 633 cc four-cylinder engine producing 21 horsepower. Production at Fiat's Mirafiori plant in ran until 1969, with 2,695,197 units built there alone, contributing to over 3 million total examples including licensed variants worldwide. A notable derivative, the Fiat 600 Multipla launched in 1956, is recognized as the first multi-purpose vehicle (MPV), offering seating for six in a boxy, forward-control design that prioritized interior space over conventional styling. In 2023, Fiat revived the 600 nameplate for a new , available in mild-hybrid and full-electric versions as of , blending retro-inspired styling with modern efficiency and features for urban driving. The , a licensed Spanish adaptation of the , entered production in under a government-backed initiative to foster domestic and entered full-scale output by 1960. Manufactured until at SEAT's Zona Franca plant in , it totaled 794,434 units, becoming the most produced model in Spanish automotive at the time. This vehicle symbolized Spain's "" during the late Franco era, embodying mass motorization and rising consumer prosperity as household incomes grew and import barriers eased. Other models bearing the 600 designation include the BMW 600, a microcar produced from 1957 to 1959 as an extension of BMW's earlier Isetta bubble car, with a 582 cc two-stroke twin-cylinder engine and limited output of approximately 35,000 units aimed at budget-conscious families. In the broader context of 1950s microcars, the Messerschmitt KR200 (1955–1964) exemplified the era's trend toward ultra-compact, fuel-efficient designs, powered by a 191 cc two-stroke engine achieving a top speed of about 56 mph, though not directly named for 600. The and models emerged as quintessential "people's cars" in , democratizing urban mobility for the and fostering a shift toward consumer culture in recovering economies, with their simple mechanics enabling widespread ownership despite modest financing options around credit scores of 600.

Sports and Events

The is an annual race covering 600 miles at in , making it the longest event in the series since its inception in 1960 as the World 600. The race consists of 400 laps on the 1.5-mile quad-oval track and is traditionally held on weekend, often starting in the evening to honor with a pre-race flyover by the U.S. Thunderbirds. holds the record for most victories with four wins, achieved in 2003, 2004, 2005, and 2014, including three consecutive triumphs that highlighted his dominance on intermediate tracks. In 2024, Christopher Bell claimed his first win in a rain-shortened event after leading 90 laps, with the race called after 249 laps due to persistent weather. On May 25, 2025, won the event. In , the 600-meter hurdles serve as a rare variant of middle-distance , primarily contested in high school indoor competitions , where it tests a blend of speed and endurance over 35-inch hurdles spaced approximately 35 meters apart. This event, less common than the standard 400-meter hurdles, emphasizes tactical pacing and has been featured in youth athletics to build versatility for longer races. In cricket, a team innings total exceeding 600 runs represents an uncommon but significant milestone in Test matches, achieved by various sides to dominate opponents and often leading to victories or draws on favorable pitches. Australia holds the record for the most such totals with 35 instances across their Test history, underscoring their batting prowess in long-form play. The year 600 AD, a in the that began on a Friday, occurred amid escalating tensions between the and the , setting the stage for the devastating Byzantine–Sasanian War of 602–628, which would exhaust both powers and pave the way for Arab conquests.

Notable Integers in the 600s

600–609

600 is a , the product of two consecutive integers 24 and 25. In the visible spectrum, light with a wavelength of 600 nm corresponds to orange color. 601 is a and forms a pair with 599, as the two differ by 2. 602 is an even with prime 2×7×432 \times 7 \times 43. 603 is a composite number divisible by 3, with prime factorization 32×673^2 \times 67. 604 is a with prime factorization 22×1512^2 \times 151, and it serves as the area code for , , . 605 is a ending in 05 and thus divisible by 5, with prime factorization 5×1125 \times 11^2. 606 is a composite number divisible by 2, 3, and 101, with prime factorization 2×3×1012 \times 3 \times 101. In the year 606 AD, died after a two-year reign, and the of Aquileia was elevated to status. 607 is a , notable as the smallest prime expressible as the sum of eleven consecutive numbers (from the third to the thirteenth). 608 is a composite number with prime factorization 25×192^5 \times 19. (calculated for 608) 609 is a composite number with prime factorization 3×7×293 \times 7 \times 29.

610–619

610 is a with the prime factorization 2×5×612 \times 5 \times 61. The year 610 AD is notable in Islamic history as the time when , at age 40, received his first revelation from the angel while meditating in the of Hira near . 611 is a with the prime 13×4713 \times 47. In , 611 equals the (numerical value) of the Hebrew word "" (תורה: tav=400, vav=6, resh=200, heh=5), symbolizing the 611 commandments transmitted through , excluding the first two given directly by at Sinai. 612 is a with the prime 22×32×172^2 \times 3^2 \times 17. 613 is a prime number. In Judaism, 613 refers to the total number of mitzvot (commandments) in the Torah, as enumerated by the medieval scholar in his Sefer HaMitzvot, comprising 248 positive and 365 negative precepts derived from biblical texts. 614 is an even with the prime 2×3072 \times 307. 615 is a with the prime 3×5×413 \times 5 \times 41, making it divisible by the small primes 3, 5, and 41. 616 is a with the prime factorization 23×7×112^3 \times 7 \times 11. In biblical scholarship, 616 appears as a variant of the "" in some ancient manuscripts of the (13:18), such as Papyrus 115 and , differing from the more common 666; this may reflect a of " Caesar" in Latin or Hebrew . 617 is a . Together with 613, it forms a pair, differing by 4, which are pairs of primes separated by multiples of 6 plus or minus 1. 618 is a with the prime factorization 2×3×1032 \times 3 \times 103. It approximates 1000 times the golden ratio conjugate ϕ−1=5−12≈0.618\phi - 1 = \frac{\sqrt{5} - 1}{2} \approx 0.618
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