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Atlas › Integer Profiles › Node 72,044,560

72,044,560

24 × 5 × 7 × 127 × 1013
Abundant Even Composite

72,044,560 factors as 2^4 × 5 × 7 × 127 × 1013. Its 80 positive divisors give a proper-divisor sum of 121,085,936, so this integer is abundant. The Collatz stopping time is 91 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 7 × 127 × 1013
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 80
Divisor Sum (σ) 193,130,496
Proper Divisor Sum 121,085,936
Digit Sum / Digital Root 28 (Root: 1)
Adjacent Primes #72044551 ← → #72044563

Radix Representation

Decimal 72044560
Binary 100010010110101000000010000 (27 bits)
Octal 0o422650020
Hexadecimal 0x44B5010

Divisor Catalog (60 of 80)

1 2 4 5 7 8 10 14 16 20 28 35 40 56 70 80 112 127 140 254 280 508 560 635 889 1,013 1,016 1,270 1,778 2,026 2,032 2,540 3,556 4,052 4,445 5,065 5,080 7,091 7,112 8,104 8,890 10,130 10,160 14,182 14,224 16,208 17,780 20,260 28,364 35,455 35,560 40,520 56,728 70,910 71,120 81,040 113,456 128,651 141,820 257,302

Collatz Trajectory (91 steps to reach 1)

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

72,044,560 36,022,280 18,011,140 9,005,570 4,502,785 13,508,356 6,754,178 3,377,089 10,131,268 5,065,634 2,532,817 7,598,452 3,799,226 1,899,613 5,698,840 2,849,420 1,424,710 712,355 2,137,066 1,068,533 3,205,600 1,602,800 801,400 400,700 200,350 100,175 300,526 150,263 450,790 225,395 676,186 338,093 1,014,280 507,140 253,570 126,785 380,356 190,178 95,089 285,268 142,634 71,317 213,952 106,976 53,488 26,744 13,372 6,686 3,343 10,030 5,015 15,046 7,523 22,570 11,285 33,856 16,928 8,464 4,232 2,116

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