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Atlas › Integer Profiles › Node 80,243,772

80,243,772

22 × 3 × 72 × 239 × 571
Abundant Even Composite

80,243,772 factors as 2^2 × 3 × 7^2 × 239 × 571. Its 72 positive divisors give a proper-divisor sum of 138,855,108, so this integer is abundant. The Collatz stopping time is 192 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 7^2 × 239 × 571
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 219,098,880
Proper Divisor Sum 138,855,108
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #80243771 ← → #80243773

Radix Representation

Decimal 80243772
Binary 100110010000110110000111100 (27 bits)
Octal 0o462066074
Hexadecimal 0x4C86C3C

Divisor Catalog (60 of 72)

1 2 3 4 6 7 12 14 21 28 42 49 84 98 147 196 239 294 478 571 588 717 956 1,142 1,434 1,673 1,713 2,284 2,868 3,346 3,426 3,997 5,019 6,692 6,852 7,994 10,038 11,711 11,991 15,988 20,076 23,422 23,982 27,979 35,133 46,844 47,964 55,958 70,266 83,937 111,916 136,469 140,532 167,874 272,938 335,748 409,407 545,876 818,814 955,283

Collatz Trajectory (192 steps to reach 1)

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

80,243,772 40,121,886 20,060,943 60,182,830 30,091,415 90,274,246 45,137,123 135,411,370 67,705,685 203,117,056 101,558,528 50,779,264 25,389,632 12,694,816 6,347,408 3,173,704 1,586,852 793,426 396,713 1,190,140 595,070 297,535 892,606 446,303 1,338,910 669,455 2,008,366 1,004,183 3,012,550 1,506,275 4,518,826 2,259,413 6,778,240 3,389,120 1,694,560 847,280 423,640 211,820 105,910 52,955 158,866 79,433 238,300 119,150 59,575 178,726 89,363 268,090 134,045 402,136 201,068 100,534 50,267 150,802 75,401 226,204 113,102 56,551 169,654 84,827

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