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9,767,680

28 × 5 × 13 × 587
Abundant Even Composite

9,767,680 factors as 2^8 × 5 × 13 × 587. Its 72 positive divisors give a proper-divisor sum of 15,471,632, so this integer is abundant. The Collatz stopping time is 62 steps.

Prime Factor Structure

Factorization String 2^8 × 5 × 13 × 587
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 25,239,312
Proper Divisor Sum 15,471,632
Digit Sum / Digital Root 43 (Root: 7)
Adjacent Primes #9767677 ← → #9767699

Radix Representation

Decimal 9767680
Binary 100101010000101100000000 (24 bits)
Octal 0o45205400
Hexadecimal 0x950B00

Divisor Catalog (60 of 72)

1 2 4 5 8 10 13 16 20 26 32 40 52 64 65 80 104 128 130 160 208 256 260 320 416 520 587 640 832 1,040 1,174 1,280 1,664 2,080 2,348 2,935 3,328 4,160 4,696 5,870 7,631 8,320 9,392 11,740 15,262 16,640 18,784 23,480 30,524 37,568 38,155 46,960 61,048 75,136 76,310 93,920 122,096 150,272 152,620 187,840

Collatz Trajectory (62 steps to reach 1)

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

9,767,680 4,883,840 2,441,920 1,220,960 610,480 305,240 152,620 76,310 38,155 114,466 57,233 171,700 85,850 42,925 128,776 64,388 32,194 16,097 48,292 24,146 12,073 36,220 18,110 9,055 27,166 13,583 40,750 20,375 61,126 30,563 91,690 45,845 137,536 68,768 34,384 17,192 8,596 4,298 2,149 6,448 3,224 1,612 806 403 1,210 605 1,816 908 454 227 682 341 1,024 512 256 128 64 32 16 8

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