λ
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Atlas › Integer Profiles › Node 57,728,960

57,728,960

26 × 5 × 89 × 2027
Abundant Even Composite

57,728,960 factors as 2^6 × 5 × 89 × 2027. Its 56 positive divisors give a proper-divisor sum of 81,351,280, so this integer is abundant. The Collatz stopping time is 176 steps.

Prime Factor Structure

Factorization String 2^6 × 5 × 89 × 2027
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 56
Divisor Sum (σ) 139,080,240
Proper Divisor Sum 81,351,280
Digit Sum / Digital Root 44 (Root: 8)
Adjacent Primes #57728959 ← → #57728971

Radix Representation

Decimal 57728960
Binary 11011100001101111111000000 (26 bits)
Octal 0o334157700
Hexadecimal 0x370DFC0

Divisor Catalog (56)

1 2 4 5 8 10 16 20 32 40 64 80 89 160 178 320 356 445 712 890 1,424 1,780 2,027 2,848 3,560 4,054 5,696 7,120 8,108 10,135 14,240 16,216 20,270 28,480 32,432 40,540 64,864 81,080 129,728 162,160 180,403 324,320 360,806 648,640 721,612 902,015 1,443,224 1,804,030 2,886,448 3,608,060 5,772,896 7,216,120 11,545,792 14,432,240 28,864,480 57,728,960

Collatz Trajectory (176 steps to reach 1)

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

57,728,960 28,864,480 14,432,240 7,216,120 3,608,060 1,804,030 902,015 2,706,046 1,353,023 4,059,070 2,029,535 6,088,606 3,044,303 9,132,910 4,566,455 13,699,366 6,849,683 20,549,050 10,274,525 30,823,576 15,411,788 7,705,894 3,852,947 11,558,842 5,779,421 17,338,264 8,669,132 4,334,566 2,167,283 6,501,850 3,250,925 9,752,776 4,876,388 2,438,194 1,219,097 3,657,292 1,828,646 914,323 2,742,970 1,371,485 4,114,456 2,057,228 1,028,614 514,307 1,542,922 771,461 2,314,384 1,157,192 578,596 289,298 144,649 433,948 216,974 108,487 325,462 162,731 488,194 244,097 732,292 366,146

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