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Atlas › Integer Profiles › Node 72,375,632

72,375,632

24 × 7 × 139 × 4649
Abundant Even Composite

72,375,632 factors as 2^4 × 7 × 139 × 4649. Its 40 positive divisors give a proper-divisor sum of 89,072,368, so this integer is abundant. The Collatz stopping time is 91 steps.

Prime Factor Structure

Factorization String 2^4 × 7 × 139 × 4649
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 161,448,000
Proper Divisor Sum 89,072,368
Digit Sum / Digital Root 35 (Root: 8)
Adjacent Primes #72375623 ← → #72375637

Radix Representation

Decimal 72375632
Binary 100010100000101110101010000 (27 bits)
Octal 0o424056520
Hexadecimal 0x4505D50

Divisor Catalog (40)

1 2 4 7 8 14 16 28 56 112 139 278 556 973 1,112 1,946 2,224 3,892 4,649 7,784 9,298 15,568 18,596 32,543 37,192 65,086 74,384 130,172 260,344 520,688 646,211 1,292,422 2,584,844 4,523,477 5,169,688 9,046,954 10,339,376 18,093,908 36,187,816 72,375,632

Collatz Trajectory (91 steps to reach 1)

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

72,375,632 36,187,816 18,093,908 9,046,954 4,523,477 13,570,432 6,785,216 3,392,608 1,696,304 848,152 424,076 212,038 106,019 318,058 159,029 477,088 238,544 119,272 59,636 29,818 14,909 44,728 22,364 11,182 5,591 16,774 8,387 25,162 12,581 37,744 18,872 9,436 4,718 2,359 7,078 3,539 10,618 5,309 15,928 7,964 3,982 1,991 5,974 2,987 8,962 4,481 13,444 6,722 3,361 10,084 5,042 2,521 7,564 3,782 1,891 5,674 2,837 8,512 4,256 2,128

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