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Atlas › Integer Profiles › Node 72,043,424

72,043,424

25 × 292 × 2677
Abundant Even Composite

72,043,424 factors as 2^5 × 29^2 × 2677. Its 36 positive divisors give a proper-divisor sum of 74,906,470, so this integer is abundant. The Collatz stopping time is 140 steps.

Prime Factor Structure

Factorization String 2^5 × 29^2 × 2677
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 146,949,894
Proper Divisor Sum 74,906,470
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #72043369 ← → #72043451

Radix Representation

Decimal 72043424
Binary 100010010110100101110100000 (27 bits)
Octal 0o422645640
Hexadecimal 0x44B4BA0

Divisor Catalog (36)

1 2 4 8 16 29 32 58 116 232 464 841 928 1,682 2,677 3,364 5,354 6,728 10,708 13,456 21,416 26,912 42,832 77,633 85,664 155,266 310,532 621,064 1,242,128 2,251,357 2,484,256 4,502,714 9,005,428 18,010,856 36,021,712 72,043,424

Collatz Trajectory (140 steps to reach 1)

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

72,043,424 36,021,712 18,010,856 9,005,428 4,502,714 2,251,357 6,754,072 3,377,036 1,688,518 844,259 2,532,778 1,266,389 3,799,168 1,899,584 949,792 474,896 237,448 118,724 59,362 29,681 89,044 44,522 22,261 66,784 33,392 16,696 8,348 4,174 2,087 6,262 3,131 9,394 4,697 14,092 7,046 3,523 10,570 5,285 15,856 7,928 3,964 1,982 991 2,974 1,487 4,462 2,231 6,694 3,347 10,042 5,021 15,064 7,532 3,766 1,883 5,650 2,825 8,476 4,238 2,119

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