74,640

2⁴ × 3 × 5 × 311

74,640 factors as 2^4 × 3 × 5 × 311. Its 40 positive divisors give a proper-divisor sum of 157,488, so this integer is abundant. The Collatz stopping time is 138 steps.

Prime Factor Structure

Factorization String 2^4 × 3 × 5 × 311

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 40

Divisor Sum (σ) 232,128

Proper Divisor Sum 157,488

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #74623 ← → #74653

Radix Representation

Decimal	74640
Binary	10010001110010000 (17 bits)
Octal	0o221620
Hexadecimal	0x12390

Divisor Catalog (40)

1 2 3 4 5 6 8 10 12 15 16 20 24 30 40 48 60 80 120 240 311 622 933 1,244 1,555 1,866 2,488 3,110 3,732 4,665 4,976 6,220 7,464 9,330 12,440 14,928 18,660 24,880 37,320 74,640

Collatz Trajectory (138 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

74,640 37,320 18,660 9,330 4,665 13,996 6,998 3,499 10,498 5,249 15,748 7,874 3,937 11,812 5,906 2,953 8,860 4,430 2,215 6,646 3,323 9,970 4,985 14,956 7,478 3,739 11,218 5,609 16,828 8,414 4,207 12,622 6,311 18,934 9,467 28,402 14,201 42,604 21,302 10,651 31,954 15,977 47,932 23,966 11,983 35,950 17,975 53,926 26,963 80,890 40,445 121,336 60,668 30,334 15,167 45,502 22,751 68,254 34,127 102,382

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