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Atlas › Integer Profiles › Node 72,088,996

72,088,996

22 × 73 × 52543
Abundant Even Composite

72,088,996 factors as 2^2 × 7^3 × 52543. Its 24 positive divisors give a proper-divisor sum of 75,034,204, so this integer is abundant. The Collatz stopping time is 321 steps.

Prime Factor Structure

Factorization String 2^2 × 7^3 × 52543
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 147,123,200
Proper Divisor Sum 75,034,204
Digit Sum / Digital Root 49 (Root: 4)
Adjacent Primes #72088967 ← → #72088997

Radix Representation

Decimal 72088996
Binary 100010010111111110110100100 (27 bits)
Octal 0o422776644
Hexadecimal 0x44BFDA4

Divisor Catalog (24)

1 2 4 7 14 28 49 98 196 343 686 1,372 52,543 105,086 210,172 367,801 735,602 1,471,204 2,574,607 5,149,214 10,298,428 18,022,249 36,044,498 72,088,996

Collatz Trajectory (321 steps to reach 1)

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

72,088,996 36,044,498 18,022,249 54,066,748 27,033,374 13,516,687 40,550,062 20,275,031 60,825,094 30,412,547 91,237,642 45,618,821 136,856,464 68,428,232 34,214,116 17,107,058 8,553,529 25,660,588 12,830,294 6,415,147 19,245,442 9,622,721 28,868,164 14,434,082 7,217,041 21,651,124 10,825,562 5,412,781 16,238,344 8,119,172 4,059,586 2,029,793 6,089,380 3,044,690 1,522,345 4,567,036 2,283,518 1,141,759 3,425,278 1,712,639 5,137,918 2,568,959 7,706,878 3,853,439 11,560,318 5,780,159 17,340,478 8,670,239 26,010,718 13,005,359 39,016,078 19,508,039 58,524,118 29,262,059 87,786,178 43,893,089 131,679,268 65,839,634 32,919,817 98,759,452

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