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Atlas › Integer Profiles › Node 72,499,232

72,499,232

25 × 13 × 61 × 2857
Abundant Even Composite

72,499,232 factors as 2^5 × 13 × 61 × 2857. Its 48 positive divisors give a proper-divisor sum of 83,787,640, so this integer is abundant. The Collatz stopping time is 184 steps.

Prime Factor Structure

Factorization String 2^5 × 13 × 61 × 2857
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 156,286,872
Proper Divisor Sum 83,787,640
Digit Sum / Digital Root 38 (Root: 2)
Adjacent Primes #72499213 ← → #72499249

Radix Representation

Decimal 72499232
Binary 100010100100100000000100000 (27 bits)
Octal 0o424440040
Hexadecimal 0x4524020

Divisor Catalog (48)

1 2 4 8 13 16 26 32 52 61 104 122 208 244 416 488 793 976 1,586 1,952 2,857 3,172 5,714 6,344 11,428 12,688 22,856 25,376 37,141 45,712 74,282 91,424 148,564 174,277 297,128 348,554 594,256 697,108 1,188,512 1,394,216 2,265,601 2,788,432 4,531,202 5,576,864 9,062,404 18,124,808 36,249,616 72,499,232

Collatz Trajectory (184 steps to reach 1)

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

72,499,232 36,249,616 18,124,808 9,062,404 4,531,202 2,265,601 6,796,804 3,398,402 1,699,201 5,097,604 2,548,802 1,274,401 3,823,204 1,911,602 955,801 2,867,404 1,433,702 716,851 2,150,554 1,075,277 3,225,832 1,612,916 806,458 403,229 1,209,688 604,844 302,422 151,211 453,634 226,817 680,452 340,226 170,113 510,340 255,170 127,585 382,756 191,378 95,689 287,068 143,534 71,767 215,302 107,651 322,954 161,477 484,432 242,216 121,108 60,554 30,277 90,832 45,416 22,708 11,354 5,677 17,032 8,516 4,258 2,129

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