λ
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Atlas › Integer Profiles › Node 72,123,720

72,123,720

23 × 3 × 5 × 601031
Abundant Even Composite

72,123,720 factors as 2^3 × 3 × 5 × 601031. Its 32 positive divisors give a proper-divisor sum of 144,247,800, so this integer is abundant. The Collatz stopping time is 215 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 5 × 601031
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 216,371,520
Proper Divisor Sum 144,247,800
Digit Sum / Digital Root 24 (Root: 6)
Adjacent Primes #72123703 ← → #72123757

Radix Representation

Decimal 72123720
Binary 100010011001000010101001000 (27 bits)
Octal 0o423102510
Hexadecimal 0x44C8548

Divisor Catalog (32)

1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 601,031 1,202,062 1,803,093 2,404,124 3,005,155 3,606,186 4,808,248 6,010,310 7,212,372 9,015,465 12,020,620 14,424,744 18,030,930 24,041,240 36,061,860 72,123,720

Collatz Trajectory (215 steps to reach 1)

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

72,123,720 36,061,860 18,030,930 9,015,465 27,046,396 13,523,198 6,761,599 20,284,798 10,142,399 30,427,198 15,213,599 45,640,798 22,820,399 68,461,198 34,230,599 102,691,798 51,345,899 154,037,698 77,018,849 231,056,548 115,528,274 57,764,137 173,292,412 86,646,206 43,323,103 129,969,310 64,984,655 194,953,966 97,476,983 292,430,950 146,215,475 438,646,426 219,323,213 657,969,640 328,984,820 164,492,410 82,246,205 246,738,616 123,369,308 61,684,654 30,842,327 92,526,982 46,263,491 138,790,474 69,395,237 208,185,712 104,092,856 52,046,428 26,023,214 13,011,607 39,034,822 19,517,411 58,552,234 29,276,117 87,828,352 43,914,176 21,957,088 10,978,544 5,489,272 2,744,636

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