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Atlas › Integer Profiles › Node 54,034,144

54,034,144

25 × 43 × 107 × 367
Abundant Even Composite

54,034,144 factors as 2^5 × 43 × 107 × 367. Its 48 positive divisors give a proper-divisor sum of 56,136,224, so this integer is abundant. The Collatz stopping time is 88 steps.

Prime Factor Structure

Factorization String 2^5 × 43 × 107 × 367
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 110,170,368
Proper Divisor Sum 56,136,224
Digit Sum / Digital Root 25 (Root: 7)
Adjacent Primes #54034133 ← → #54034151

Radix Representation

Decimal 54034144
Binary 11001110000111111011100000 (26 bits)
Octal 0o316077340
Hexadecimal 0x3387EE0

Divisor Catalog (48)

1 2 4 8 16 32 43 86 107 172 214 344 367 428 688 734 856 1,376 1,468 1,712 2,936 3,424 4,601 5,872 9,202 11,744 15,781 18,404 31,562 36,808 39,269 63,124 73,616 78,538 126,248 147,232 157,076 252,496 314,152 504,992 628,304 1,256,608 1,688,567 3,377,134 6,754,268 13,508,536 27,017,072 54,034,144

Collatz Trajectory (88 steps to reach 1)

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

54,034,144 27,017,072 13,508,536 6,754,268 3,377,134 1,688,567 5,065,702 2,532,851 7,598,554 3,799,277 11,397,832 5,698,916 2,849,458 1,424,729 4,274,188 2,137,094 1,068,547 3,205,642 1,602,821 4,808,464 2,404,232 1,202,116 601,058 300,529 901,588 450,794 225,397 676,192 338,096 169,048 84,524 42,262 21,131 63,394 31,697 95,092 47,546 23,773 71,320 35,660 17,830 8,915 26,746 13,373 40,120 20,060 10,030 5,015 15,046 7,523 22,570 11,285 33,856 16,928 8,464 4,232 2,116 1,058 529 1,588

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