80,960,460

2² × 3 × 5 × 7 × 17² × 23 × 29

80,960,460 factors as 2^2 × 3 × 5 × 7 × 17^2 × 23 × 29. Its 288 positive divisors give a proper-divisor sum of 216,117,300, so this integer is abundant. The Collatz stopping time is 223 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 5 × 7 × 17^2 × 23 × 29

Distinct Prime Factors 7

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 288

Divisor Sum (σ) 297,077,760

Proper Divisor Sum 216,117,300

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #80960459 ← → #80960471

Radix Representation

Decimal	80960460
Binary	100110100110101101111001100 (27 bits)
Octal	0o464655714
Hexadecimal	0x4D35BCC

Divisor Catalog (60 of 288)

1 2 3 4 5 6 7 10 12 14 15 17 20 21 23 28 29 30 34 35 42 46 51 58 60 68 69 70 84 85 87 92 102 105 115 116 119 138 140 145 161 170 174 203 204 210 230 238 255 276 289 290 322 340 345 348 357 391 406 420

Collatz Trajectory (223 steps to reach 1)

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

80,960,460 40,480,230 20,240,115 60,720,346 30,360,173 91,080,520 45,540,260 22,770,130 11,385,065 34,155,196 17,077,598 8,538,799 25,616,398 12,808,199 38,424,598 19,212,299 57,636,898 28,818,449 86,455,348 43,227,674 21,613,837 64,841,512 32,420,756 16,210,378 8,105,189 24,315,568 12,157,784 6,078,892 3,039,446 1,519,723 4,559,170 2,279,585 6,838,756 3,419,378 1,709,689 5,129,068 2,564,534 1,282,267 3,846,802 1,923,401 5,770,204 2,885,102 1,442,551 4,327,654 2,163,827 6,491,482 3,245,741 9,737,224 4,868,612 2,434,306 1,217,153 3,651,460 1,825,730 912,865 2,738,596 1,369,298 684,649 2,053,948 1,026,974 513,487

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