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Atlas › Integer Profiles › Node 57,736,100

57,736,100

22 × 52 × 29 × 43 × 463
Abundant Even Composite

57,736,100 factors as 2^2 × 5^2 × 29 × 43 × 463. Its 72 positive divisors give a proper-divisor sum of 75,172,060, so this integer is abundant. The Collatz stopping time is 238 steps.

Prime Factor Structure

Factorization String 2^2 × 5^2 × 29 × 43 × 463
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 132,908,160
Proper Divisor Sum 75,172,060
Digit Sum / Digital Root 29 (Root: 2)
Adjacent Primes #57736099 ← → #57736103

Radix Representation

Decimal 57736100
Binary 11011100001111101110100100 (26 bits)
Octal 0o334175644
Hexadecimal 0x370FBA4

Divisor Catalog (60 of 72)

1 2 4 5 10 20 25 29 43 50 58 86 100 116 145 172 215 290 430 463 580 725 860 926 1,075 1,247 1,450 1,852 2,150 2,315 2,494 2,900 4,300 4,630 4,988 6,235 9,260 11,575 12,470 13,427 19,909 23,150 24,940 26,854 31,175 39,818 46,300 53,708 62,350 67,135 79,636 99,545 124,700 134,270 199,090 268,540 335,675 398,180 497,725 577,361

Collatz Trajectory (238 steps to reach 1)

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

57,736,100 28,868,050 14,434,025 43,302,076 21,651,038 10,825,519 32,476,558 16,238,279 48,714,838 24,357,419 73,072,258 36,536,129 109,608,388 54,804,194 27,402,097 82,206,292 41,103,146 20,551,573 61,654,720 30,827,360 15,413,680 7,706,840 3,853,420 1,926,710 963,355 2,890,066 1,445,033 4,335,100 2,167,550 1,083,775 3,251,326 1,625,663 4,876,990 2,438,495 7,315,486 3,657,743 10,973,230 5,486,615 16,459,846 8,229,923 24,689,770 12,344,885 37,034,656 18,517,328 9,258,664 4,629,332 2,314,666 1,157,333 3,472,000 1,736,000 868,000 434,000 217,000 108,500 54,250 27,125 81,376 40,688 20,344 10,172

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