52,591,872

2⁸ × 3 × 31 × 47²

52,591,872 factors as 2^8 × 3 × 31 × 47^2. Its 108 positive divisors give a proper-divisor sum of 95,033,984, so this integer is abundant. The Collatz stopping time is 318 steps.

Prime Factor Structure

Factorization String 2^8 × 3 × 31 × 47^2

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 108

Divisor Sum (σ) 147,625,856

Proper Divisor Sum 95,033,984

Digit Sum / Digital Root 39 (Root: 3)

Adjacent Primes #52591853 ← → #52591879

Radix Representation

Decimal	52591872
Binary	11001000100111110100000000 (26 bits)
Octal	0o310476400
Hexadecimal	0x3227D00

Divisor Catalog (60 of 108)

1 2 3 4 6 8 12 16 24 31 32 47 48 62 64 93 94 96 124 128 141 186 188 192 248 256 282 372 376 384 496 564 744 752 768 992 1,128 1,457 1,488 1,504 1,984 2,209 2,256 2,914 2,976 3,008 3,968 4,371 4,418 4,512 5,828 5,952 6,016 6,627 7,936 8,742 8,836 9,024 11,656 11,904

Collatz Trajectory (318 steps to reach 1)

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

52,591,872 26,295,936 13,147,968 6,573,984 3,286,992 1,643,496 821,748 410,874 205,437 616,312 308,156 154,078 77,039 231,118 115,559 346,678 173,339 520,018 260,009 780,028 390,014 195,007 585,022 292,511 877,534 438,767 1,316,302 658,151 1,974,454 987,227 2,961,682 1,480,841 4,442,524 2,221,262 1,110,631 3,331,894 1,665,947 4,997,842 2,498,921 7,496,764 3,748,382 1,874,191 5,622,574 2,811,287 8,433,862 4,216,931 12,650,794 6,325,397 18,976,192 9,488,096 4,744,048 2,372,024 1,186,012 593,006 296,503 889,510 444,755 1,334,266 667,133 2,001,400

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