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Atlas › Integer Profiles › Node 72,047,064

72,047,064

23 × 3 × 229 × 13109
Abundant Even Composite

72,047,064 factors as 2^3 × 3 × 229 × 13109. Its 32 positive divisors give a proper-divisor sum of 108,870,936, so this integer is abundant. The Collatz stopping time is 202 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 229 × 13109
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 180,918,000
Proper Divisor Sum 108,870,936
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #72047051 ← → #72047081

Radix Representation

Decimal 72047064
Binary 100010010110101100111011000 (27 bits)
Octal 0o422654730
Hexadecimal 0x44B59D8

Divisor Catalog (32)

1 2 3 4 6 8 12 24 229 458 687 916 1,374 1,832 2,748 5,496 13,109 26,218 39,327 52,436 78,654 104,872 157,308 314,616 3,001,961 6,003,922 9,005,883 12,007,844 18,011,766 24,015,688 36,023,532 72,047,064

Collatz Trajectory (202 steps to reach 1)

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

72,047,064 36,023,532 18,011,766 9,005,883 27,017,650 13,508,825 40,526,476 20,263,238 10,131,619 30,394,858 15,197,429 45,592,288 22,796,144 11,398,072 5,699,036 2,849,518 1,424,759 4,274,278 2,137,139 6,411,418 3,205,709 9,617,128 4,808,564 2,404,282 1,202,141 3,606,424 1,803,212 901,606 450,803 1,352,410 676,205 2,028,616 1,014,308 507,154 253,577 760,732 380,366 190,183 570,550 285,275 855,826 427,913 1,283,740 641,870 320,935 962,806 481,403 1,444,210 722,105 2,166,316 1,083,158 541,579 1,624,738 812,369 2,437,108 1,218,554 609,277 1,827,832 913,916 456,958

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