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Atlas › Integer Profiles › Node 54,500,784

54,500,784

24 × 3 × 13 × 167 × 523
Abundant Even Composite

54,500,784 factors as 2^4 × 3 × 13 × 167 × 523. Its 80 positive divisors give a proper-divisor sum of 98,322,768, so this integer is abundant. The Collatz stopping time is 181 steps.

Prime Factor Structure

Factorization String 2^4 × 3 × 13 × 167 × 523
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 80
Divisor Sum (σ) 152,823,552
Proper Divisor Sum 98,322,768
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #54500783 ← → #54500791

Radix Representation

Decimal 54500784
Binary 11001111111001110110110000 (26 bits)
Octal 0o317716660
Hexadecimal 0x33F9DB0

Divisor Catalog (60 of 80)

1 2 3 4 6 8 12 13 16 24 26 39 48 52 78 104 156 167 208 312 334 501 523 624 668 1,002 1,046 1,336 1,569 2,004 2,092 2,171 2,672 3,138 4,008 4,184 4,342 6,276 6,513 6,799 8,016 8,368 8,684 12,552 13,026 13,598 17,368 20,397 25,104 26,052 27,196 34,736 40,794 52,104 54,392 81,588 87,341 104,208 108,784 163,176

Collatz Trajectory (181 steps to reach 1)

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

54,500,784 27,250,392 13,625,196 6,812,598 3,406,299 10,218,898 5,109,449 15,328,348 7,664,174 3,832,087 11,496,262 5,748,131 17,244,394 8,622,197 25,866,592 12,933,296 6,466,648 3,233,324 1,616,662 808,331 2,424,994 1,212,497 3,637,492 1,818,746 909,373 2,728,120 1,364,060 682,030 341,015 1,023,046 511,523 1,534,570 767,285 2,301,856 1,150,928 575,464 287,732 143,866 71,933 215,800 107,900 53,950 26,975 80,926 40,463 121,390 60,695 182,086 91,043 273,130 136,565 409,696 204,848 102,424 51,212 25,606 12,803 38,410 19,205 57,616

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