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Atlas › Integer Profiles › Node 37,123,712

37,123,712

27 × 29 × 73 × 137
Abundant Even Composite

37,123,712 factors as 2^7 × 29 × 73 × 137. Its 64 positive divisors give a proper-divisor sum of 40,998,088, so this integer is abundant. The Collatz stopping time is 196 steps.

Prime Factor Structure

Factorization String 2^7 × 29 × 73 × 137
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 78,121,800
Proper Divisor Sum 40,998,088
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #37123711 ← → #37123717

Radix Representation

Decimal 37123712
Binary 10001101100111011010000000 (26 bits)
Octal 0o215473200
Hexadecimal 0x2367680

Divisor Catalog (60 of 64)

1 2 4 8 16 29 32 58 64 73 116 128 137 146 232 274 292 464 548 584 928 1,096 1,168 1,856 2,117 2,192 2,336 3,712 3,973 4,234 4,384 4,672 7,946 8,468 8,768 9,344 10,001 15,892 16,936 17,536 20,002 31,784 33,872 40,004 63,568 67,744 80,008 127,136 135,488 160,016 254,272 270,976 290,029 320,032 508,544 580,058 640,064 1,160,116 1,280,128 2,320,232

Collatz Trajectory (196 steps to reach 1)

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

37,123,712 18,561,856 9,280,928 4,640,464 2,320,232 1,160,116 580,058 290,029 870,088 435,044 217,522 108,761 326,284 163,142 81,571 244,714 122,357 367,072 183,536 91,768 45,884 22,942 11,471 34,414 17,207 51,622 25,811 77,434 38,717 116,152 58,076 29,038 14,519 43,558 21,779 65,338 32,669 98,008 49,004 24,502 12,251 36,754 18,377 55,132 27,566 13,783 41,350 20,675 62,026 31,013 93,040 46,520 23,260 11,630 5,815 17,446 8,723 26,170 13,085 39,256

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