752,640

2¹⁰ × 3 × 5 × 7²

Prime Factor Structure

Factorization String 2^10 × 3 × 5 × 7^2

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 132

Divisor Sum (σ) 2,800,296

Proper Divisor Sum 2,047,656

Digit Sum / Digital Root 24 (Root: 6)

Adjacent Primes #752639 ← → #752651

Radix Representation

Decimal	752640
Binary	10110111110000000000 (20 bits)
Octal	0o2676000
Hexadecimal	0xB7C00

Divisor Catalog (60 of 132)

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 64 70 80 84 96 98 105 112 120 128 140 147 160 168 192 196 210 224 240 245 256 280 294 320 336 384 392 420 448 480 490 512 560 588

Collatz Trajectory (56 steps to reach 1)

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

752,640 376,320 188,160 94,080 47,040 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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