23,520

2⁵ × 3 × 5 × 7²

23,520 factors as 2^5 × 3 × 5 × 7^2. Its 72 positive divisors give a proper-divisor sum of 62,664, so this integer is abundant. The Collatz stopping time is 51 steps.

Prime Factor Structure

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

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 86,184

Proper Divisor Sum 62,664

Digit Sum / Digital Root 12 (Root: 3)

Adjacent Primes #23509 ← → #23531

Radix Representation

Decimal	23520
Binary	101101111100000 (15 bits)
Octal	0o55740
Hexadecimal	0x5BE0

Divisor Catalog (60 of 72)

1 2 3 4 5 6 7 8 10 12 14 15 16 20 21 24 28 30 32 35 40 42 48 49 56 60 70 80 84 96 98 105 112 120 140 147 160 168 196 210 224 240 245 280 294 336 392 420 480 490 560 588 672 735 784 840 980 1,120 1,176 1,470

Collatz Trajectory (51 steps to reach 1)

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

23,520 11,760 5,880 2,940 1,470 735 2,206 1,103 3,310 1,655 4,966 2,483 7,450 3,725 11,176 5,588 2,794 1,397 4,192 2,096 1,048 524 262 131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

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