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Atlas › Integer Profiles › Node 72,088,268

72,088,268

22 × 7 × 31 × 53 × 1567
Abundant Even Composite

72,088,268 factors as 2^2 × 7 × 31 × 53 × 1567. Its 48 positive divisors give a proper-divisor sum of 79,643,956, so this integer is abundant. The Collatz stopping time is 321 steps.

Prime Factor Structure

Factorization String 2^2 × 7 × 31 × 53 × 1567
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 151,732,224
Proper Divisor Sum 79,643,956
Digit Sum / Digital Root 41 (Root: 5)
Adjacent Primes #72088267 ← → #72088283

Radix Representation

Decimal 72088268
Binary 100010010111111101011001100 (27 bits)
Octal 0o422775314
Hexadecimal 0x44BFACC

Divisor Catalog (48)

1 2 4 7 14 28 31 53 62 106 124 212 217 371 434 742 868 1,484 1,567 1,643 3,134 3,286 6,268 6,572 10,969 11,501 21,938 23,002 43,876 46,004 48,577 83,051 97,154 166,102 194,308 332,204 340,039 581,357 680,078 1,162,714 1,360,156 2,325,428 2,574,581 5,149,162 10,298,324 18,022,067 36,044,134 72,088,268

Collatz Trajectory (321 steps to reach 1)

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

72,088,268 36,044,134 18,022,067 54,066,202 27,033,101 81,099,304 40,549,652 20,274,826 10,137,413 30,412,240 15,206,120 7,603,060 3,801,530 1,900,765 5,702,296 2,851,148 1,425,574 712,787 2,138,362 1,069,181 3,207,544 1,603,772 801,886 400,943 1,202,830 601,415 1,804,246 902,123 2,706,370 1,353,185 4,059,556 2,029,778 1,014,889 3,044,668 1,522,334 761,167 2,283,502 1,141,751 3,425,254 1,712,627 5,137,882 2,568,941 7,706,824 3,853,412 1,926,706 963,353 2,890,060 1,445,030 722,515 2,167,546 1,083,773 3,251,320 1,625,660 812,830 406,415 1,219,246 609,623 1,828,870 914,435 2,743,306

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