λ
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Atlas › Integer Profiles › Node 72,246,768

72,246,768

24 × 3 × 11 × 293 × 467
Abundant Even Composite

72,246,768 factors as 2^4 × 3 × 11 × 293 × 467. Its 80 positive divisors give a proper-divisor sum of 132,490,128, so this integer is abundant. The Collatz stopping time is 259 steps.

Prime Factor Structure

Factorization String 2^4 × 3 × 11 × 293 × 467
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 80
Divisor Sum (σ) 204,736,896
Proper Divisor Sum 132,490,128
Digit Sum / Digital Root 42 (Root: 6)
Adjacent Primes #72246767 ← → #72246773

Radix Representation

Decimal 72246768
Binary 100010011100110010111110000 (27 bits)
Octal 0o423462760
Hexadecimal 0x44E65F0

Divisor Catalog (60 of 80)

1 2 3 4 6 8 11 12 16 22 24 33 44 48 66 88 132 176 264 293 467 528 586 879 934 1,172 1,401 1,758 1,868 2,344 2,802 3,223 3,516 3,736 4,688 5,137 5,604 6,446 7,032 7,472 9,669 10,274 11,208 12,892 14,064 15,411 19,338 20,548 22,416 25,784 30,822 38,676 41,096 51,568 61,644 77,352 82,192 123,288 136,831 154,704

Collatz Trajectory (259 steps to reach 1)

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

72,246,768 36,123,384 18,061,692 9,030,846 4,515,423 13,546,270 6,773,135 20,319,406 10,159,703 30,479,110 15,239,555 45,718,666 22,859,333 68,578,000 34,289,000 17,144,500 8,572,250 4,286,125 12,858,376 6,429,188 3,214,594 1,607,297 4,821,892 2,410,946 1,205,473 3,616,420 1,808,210 904,105 2,712,316 1,356,158 678,079 2,034,238 1,017,119 3,051,358 1,525,679 4,577,038 2,288,519 6,865,558 3,432,779 10,298,338 5,149,169 15,447,508 7,723,754 3,861,877 11,585,632 5,792,816 2,896,408 1,448,204 724,102 362,051 1,086,154 543,077 1,629,232 814,616 407,308 203,654 101,827 305,482 152,741 458,224

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