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Atlas › Integer Profiles › Node 72,044,574

72,044,574

2 × 3 × 7 × 701 × 2447
Abundant Even Composite

72,044,574 factors as 2 × 3 × 7 × 701 × 2447. Its 32 positive divisors give a proper-divisor sum of 92,931,042, so this integer is abundant. The Collatz stopping time is 140 steps.

Prime Factor Structure

Factorization String 2 × 3 × 7 × 701 × 2447
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 164,975,616
Proper Divisor Sum 92,931,042
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #72044573 ← → #72044593

Radix Representation

Decimal 72044574
Binary 100010010110101000000011110 (27 bits)
Octal 0o422650036
Hexadecimal 0x44B501E

Divisor Catalog (32)

1 2 3 6 7 14 21 42 701 1,402 2,103 2,447 4,206 4,894 4,907 7,341 9,814 14,682 14,721 17,129 29,442 34,258 51,387 102,774 1,715,347 3,430,694 5,146,041 10,292,082 12,007,429 24,014,858 36,022,287 72,044,574

Collatz Trajectory (140 steps to reach 1)

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

72,044,574 36,022,287 108,066,862 54,033,431 162,100,294 81,050,147 243,150,442 121,575,221 364,725,664 182,362,832 91,181,416 45,590,708 22,795,354 11,397,677 34,193,032 17,096,516 8,548,258 4,274,129 12,822,388 6,411,194 3,205,597 9,616,792 4,808,396 2,404,198 1,202,099 3,606,298 1,803,149 5,409,448 2,704,724 1,352,362 676,181 2,028,544 1,014,272 507,136 253,568 126,784 63,392 31,696 15,848 7,924 3,962 1,981 5,944 2,972 1,486 743 2,230 1,115 3,346 1,673 5,020 2,510 1,255 3,766 1,883 5,650 2,825 8,476 4,238 2,119

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