7,577,120

2⁵ × 5 × 23 × 29 × 71

7,577,120 factors as 2^5 × 5 × 23 × 29 × 71. Its 96 positive divisors give a proper-divisor sum of 12,018,400, so this integer is abundant. The Collatz stopping time is 103 steps.

Prime Factor Structure

Factorization String 2^5 × 5 × 23 × 29 × 71

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 19,595,520

Proper Divisor Sum 12,018,400

Digit Sum / Digital Root 29 (Root: 2)

Adjacent Primes #7577117 ← → #7577123

Radix Representation

Decimal	7577120
Binary	11100111001111000100000 (23 bits)
Octal	0o34717040
Hexadecimal	0x739E20

Divisor Catalog (60 of 96)

1 2 4 5 8 10 16 20 23 29 32 40 46 58 71 80 92 115 116 142 145 160 184 230 232 284 290 355 368 460 464 568 580 667 710 736 920 928 1,136 1,160 1,334 1,420 1,633 1,840 2,059 2,272 2,320 2,668 2,840 3,266 3,335 3,680 4,118 4,640 5,336 5,680 6,532 6,670 8,165 8,236

Collatz Trajectory (103 steps to reach 1)

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

7,577,120 3,788,560 1,894,280 947,140 473,570 236,785 710,356 355,178 177,589 532,768 266,384 133,192 66,596 33,298 16,649 49,948 24,974 12,487 37,462 18,731 56,194 28,097 84,292 42,146 21,073 63,220 31,610 15,805 47,416 23,708 11,854 5,927 17,782 8,891 26,674 13,337 40,012 20,006 10,003 30,010 15,005 45,016 22,508 11,254 5,627 16,882 8,441 25,324 12,662 6,331 18,994 9,497 28,492 14,246 7,123 21,370 10,685 32,056 16,028 8,014

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