51,744

2⁵ × 3 × 7² × 11

51,744 factors as 2^5 × 3 × 7^2 × 11. Its 72 positive divisors give a proper-divisor sum of 120,624, so this integer is abundant. The Collatz stopping time is 52 steps.

Prime Factor Structure

Factorization String 2^5 × 3 × 7^2 × 11

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 172,368

Proper Divisor Sum 120,624

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #51721 ← → #51749

Radix Representation

Decimal	51744
Binary	1100101000100000 (16 bits)
Octal	0o145040
Hexadecimal	0xCA20

Divisor Catalog (60 of 72)

1 2 3 4 6 7 8 11 12 14 16 21 22 24 28 32 33 42 44 48 49 56 66 77 84 88 96 98 112 132 147 154 168 176 196 224 231 264 294 308 336 352 392 462 528 539 588 616 672 784 924 1,056 1,078 1,176 1,232 1,568 1,617 1,848 2,156 2,352

Collatz Trajectory (52 steps to reach 1)

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

51,744 25,872 12,936 6,468 3,234 1,617 4,852 2,426 1,213 3,640 1,820 910 455 1,366 683 2,050 1,025 3,076 1,538 769 2,308 1,154 577 1,732 866 433 1,300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1

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