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Atlas › Integer Profiles › Node 47,733,784

47,733,784

23 × 7 × 432 × 461
Abundant Even Composite

47,733,784 factors as 2^3 × 7 × 43^2 × 461. Its 48 positive divisors give a proper-divisor sum of 57,214,136, so this integer is abundant. The Collatz stopping time is 155 steps.

Prime Factor Structure

Factorization String 2^3 × 7 × 43^2 × 461
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 104,947,920
Proper Divisor Sum 57,214,136
Digit Sum / Digital Root 43 (Root: 7)
Adjacent Primes #47733767 ← → #47733793

Radix Representation

Decimal 47733784
Binary 10110110000101110000011000 (26 bits)
Octal 0o266056030
Hexadecimal 0x2D85C18

Divisor Catalog (48)

1 2 4 7 8 14 28 43 56 86 172 301 344 461 602 922 1,204 1,844 1,849 2,408 3,227 3,688 3,698 6,454 7,396 12,908 12,943 14,792 19,823 25,816 25,886 39,646 51,772 79,292 103,544 138,761 158,584 277,522 555,044 852,389 1,110,088 1,704,778 3,409,556 5,966,723 6,819,112 11,933,446 23,866,892 47,733,784

Collatz Trajectory (155 steps to reach 1)

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

47,733,784 23,866,892 11,933,446 5,966,723 17,900,170 8,950,085 26,850,256 13,425,128 6,712,564 3,356,282 1,678,141 5,034,424 2,517,212 1,258,606 629,303 1,887,910 943,955 2,831,866 1,415,933 4,247,800 2,123,900 1,061,950 530,975 1,592,926 796,463 2,389,390 1,194,695 3,584,086 1,792,043 5,376,130 2,688,065 8,064,196 4,032,098 2,016,049 6,048,148 3,024,074 1,512,037 4,536,112 2,268,056 1,134,028 567,014 283,507 850,522 425,261 1,275,784 637,892 318,946 159,473 478,420 239,210 119,605 358,816 179,408 89,704 44,852 22,426 11,213 33,640 16,820 8,410

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