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13,655,840

25 × 5 × 11 × 7759
Abundant Even Composite

13,655,840 factors as 2^5 × 5 × 11 × 7759. Its 48 positive divisors give a proper-divisor sum of 21,543,520, so this integer is abundant. The Collatz stopping time is 179 steps.

Prime Factor Structure

Factorization String 2^5 × 5 × 11 × 7759
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 35,199,360
Proper Divisor Sum 21,543,520
Digit Sum / Digital Root 32 (Root: 5)
Adjacent Primes #13655827 ← → #13655857

Radix Representation

Decimal 13655840
Binary 110100000101111100100000 (24 bits)
Octal 0o64057440
Hexadecimal 0xD05F20

Divisor Catalog (48)

1 2 4 5 8 10 11 16 20 22 32 40 44 55 80 88 110 160 176 220 352 440 880 1,760 7,759 15,518 31,036 38,795 62,072 77,590 85,349 124,144 155,180 170,698 248,288 310,360 341,396 426,745 620,720 682,792 853,490 1,241,440 1,365,584 1,706,980 2,731,168 3,413,960 6,827,920 13,655,840

Collatz Trajectory (179 steps to reach 1)

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

13,655,840 6,827,920 3,413,960 1,706,980 853,490 426,745 1,280,236 640,118 320,059 960,178 480,089 1,440,268 720,134 360,067 1,080,202 540,101 1,620,304 810,152 405,076 202,538 101,269 303,808 151,904 75,952 37,976 18,988 9,494 4,747 14,242 7,121 21,364 10,682 5,341 16,024 8,012 4,006 2,003 6,010 3,005 9,016 4,508 2,254 1,127 3,382 1,691 5,074 2,537 7,612 3,806 1,903 5,710 2,855 8,566 4,283 12,850 6,425 19,276 9,638 4,819 14,458

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