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Atlas › Integer Profiles › Node 32,100,744

32,100,744

23 × 3 × 13 × 137 × 751
Abundant Even Composite

32,100,744 factors as 2^3 × 3 × 13 × 137 × 751. Its 64 positive divisors give a proper-divisor sum of 55,071,096, so this integer is abundant. The Collatz stopping time is 144 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 13 × 137 × 751
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 87,171,840
Proper Divisor Sum 55,071,096
Digit Sum / Digital Root 21 (Root: 3)
Adjacent Primes #32100737 ← → #32100773

Radix Representation

Decimal 32100744
Binary 1111010011101000110001000 (25 bits)
Octal 0o172350610
Hexadecimal 0x1E9D188

Divisor Catalog (60 of 64)

1 2 3 4 6 8 12 13 24 26 39 52 78 104 137 156 274 312 411 548 751 822 1,096 1,502 1,644 1,781 2,253 3,004 3,288 3,562 4,506 5,343 6,008 7,124 9,012 9,763 10,686 14,248 18,024 19,526 21,372 29,289 39,052 42,744 58,578 78,104 102,887 117,156 205,774 234,312 308,661 411,548 617,322 823,096 1,234,644 1,337,531 2,469,288 2,675,062 4,012,593 5,350,124

Collatz Trajectory (144 steps to reach 1)

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

32,100,744 16,050,372 8,025,186 4,012,593 12,037,780 6,018,890 3,009,445 9,028,336 4,514,168 2,257,084 1,128,542 564,271 1,692,814 846,407 2,539,222 1,269,611 3,808,834 1,904,417 5,713,252 2,856,626 1,428,313 4,284,940 2,142,470 1,071,235 3,213,706 1,606,853 4,820,560 2,410,280 1,205,140 602,570 301,285 903,856 451,928 225,964 112,982 56,491 169,474 84,737 254,212 127,106 63,553 190,660 95,330 47,665 142,996 71,498 35,749 107,248 53,624 26,812 13,406 6,703 20,110 10,055 30,166 15,083 45,250 22,625 67,876 33,938

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