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Atlas › Integer Profiles › Node 52,106,960

52,106,960

24 × 5 × 23 × 28319
Abundant Even Composite

52,106,960 factors as 2^4 × 5 × 23 × 28319. Its 40 positive divisors give a proper-divisor sum of 74,313,520, so this integer is abundant. The Collatz stopping time is 119 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 23 × 28319
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 126,420,480
Proper Divisor Sum 74,313,520
Digit Sum / Digital Root 29 (Root: 2)
Adjacent Primes #52106959 ← → #52106963

Radix Representation

Decimal 52106960
Binary 11000110110001011011010000 (26 bits)
Octal 0o306613320
Hexadecimal 0x31B16D0

Divisor Catalog (40)

1 2 4 5 8 10 16 20 23 40 46 80 92 115 184 230 368 460 920 1,840 28,319 56,638 113,276 141,595 226,552 283,190 453,104 566,380 651,337 1,132,760 1,302,674 2,265,520 2,605,348 3,256,685 5,210,696 6,513,370 10,421,392 13,026,740 26,053,480 52,106,960

Collatz Trajectory (119 steps to reach 1)

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

52,106,960 26,053,480 13,026,740 6,513,370 3,256,685 9,770,056 4,885,028 2,442,514 1,221,257 3,663,772 1,831,886 915,943 2,747,830 1,373,915 4,121,746 2,060,873 6,182,620 3,091,310 1,545,655 4,636,966 2,318,483 6,955,450 3,477,725 10,433,176 5,216,588 2,608,294 1,304,147 3,912,442 1,956,221 5,868,664 2,934,332 1,467,166 733,583 2,200,750 1,100,375 3,301,126 1,650,563 4,951,690 2,475,845 7,427,536 3,713,768 1,856,884 928,442 464,221 1,392,664 696,332 348,166 174,083 522,250 261,125 783,376 391,688 195,844 97,922 48,961 146,884 73,442 36,721 110,164 55,082

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