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Atlas › Integer Profiles › Node 54,822,320

54,822,320

24 × 5 × 7 × 223 × 439
Abundant Even Composite

54,822,320 factors as 2^4 × 5 × 7 × 223 × 439. Its 80 positive divisors give a proper-divisor sum of 91,834,960, so this integer is abundant. The Collatz stopping time is 168 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 7 × 223 × 439
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 80
Divisor Sum (σ) 146,657,280
Proper Divisor Sum 91,834,960
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #54822319 ← → #54822323

Radix Representation

Decimal 54822320
Binary 11010001001000010110110000 (26 bits)
Octal 0o321102660
Hexadecimal 0x34485B0

Divisor Catalog (60 of 80)

1 2 4 5 7 8 10 14 16 20 28 35 40 56 70 80 112 140 223 280 439 446 560 878 892 1,115 1,561 1,756 1,784 2,195 2,230 3,073 3,122 3,512 3,568 4,390 4,460 6,146 6,244 7,024 7,805 8,780 8,920 12,292 12,488 15,365 15,610 17,560 17,840 24,584 24,976 30,730 31,220 35,120 49,168 61,460 62,440 97,897 122,920 124,880

Collatz Trajectory (168 steps to reach 1)

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

54,822,320 27,411,160 13,705,580 6,852,790 3,426,395 10,279,186 5,139,593 15,418,780 7,709,390 3,854,695 11,564,086 5,782,043 17,346,130 8,673,065 26,019,196 13,009,598 6,504,799 19,514,398 9,757,199 29,271,598 14,635,799 43,907,398 21,953,699 65,861,098 32,930,549 98,791,648 49,395,824 24,697,912 12,348,956 6,174,478 3,087,239 9,261,718 4,630,859 13,892,578 6,946,289 20,838,868 10,419,434 5,209,717 15,629,152 7,814,576 3,907,288 1,953,644 976,822 488,411 1,465,234 732,617 2,197,852 1,098,926 549,463 1,648,390 824,195 2,472,586 1,236,293 3,708,880 1,854,440 927,220 463,610 231,805 695,416 347,708

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