λ
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Atlas › Integer Profiles › Node 36,975,624

36,975,624

23 × 3 × 7 × 97 × 2269
Abundant Even Composite

36,975,624 factors as 2^3 × 3 × 7 × 97 × 2269. Its 64 positive divisors give a proper-divisor sum of 69,805,176, so this integer is abundant. The Collatz stopping time is 196 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 7 × 97 × 2269
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 106,780,800
Proper Divisor Sum 69,805,176
Digit Sum / Digital Root 42 (Root: 6)
Adjacent Primes #36975623 ← → #36975649

Radix Representation

Decimal 36975624
Binary 10001101000011010000001000 (26 bits)
Octal 0o215032010
Hexadecimal 0x2343408

Divisor Catalog (60 of 64)

1 2 3 4 6 7 8 12 14 21 24 28 42 56 84 97 168 194 291 388 582 679 776 1,164 1,358 2,037 2,269 2,328 2,716 4,074 4,538 5,432 6,807 8,148 9,076 13,614 15,883 16,296 18,152 27,228 31,766 47,649 54,456 63,532 95,298 127,064 190,596 220,093 381,192 440,186 660,279 880,372 1,320,558 1,540,651 1,760,744 2,641,116 3,081,302 4,621,953 5,282,232 6,162,604

Collatz Trajectory (196 steps to reach 1)

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

36,975,624 18,487,812 9,243,906 4,621,953 13,865,860 6,932,930 3,466,465 10,399,396 5,199,698 2,599,849 7,799,548 3,899,774 1,949,887 5,849,662 2,924,831 8,774,494 4,387,247 13,161,742 6,580,871 19,742,614 9,871,307 29,613,922 14,806,961 44,420,884 22,210,442 11,105,221 33,315,664 16,657,832 8,328,916 4,164,458 2,082,229 6,246,688 3,123,344 1,561,672 780,836 390,418 195,209 585,628 292,814 146,407 439,222 219,611 658,834 329,417 988,252 494,126 247,063 741,190 370,595 1,111,786 555,893 1,667,680 833,840 416,920 208,460 104,230 52,115 156,346 78,173 234,520

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