680,800

2⁵ × 5² × 23 × 37

680,800 factors as 2^5 × 5^2 × 23 × 37. Its 72 positive divisors give a proper-divisor sum of 1,100,336, so this integer is abundant. The Collatz stopping time is 154 steps.

Prime Factor Structure

Factorization String 2^5 × 5^2 × 23 × 37

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 1,781,136

Proper Divisor Sum 1,100,336

Digit Sum / Digital Root 22 (Root: 4)

Adjacent Primes #680783 ← → #680803

Radix Representation

Decimal	680800
Binary	10100110001101100000 (20 bits)
Octal	0o2461540
Hexadecimal	0xA6360

Divisor Catalog (60 of 72)

1 2 4 5 8 10 16 20 23 25 32 37 40 46 50 74 80 92 100 115 148 160 184 185 200 230 296 368 370 400 460 575 592 736 740 800 851 920 925 1,150 1,184 1,480 1,702 1,840 1,850 2,300 2,960 3,404 3,680 3,700 4,255 4,600 5,920 6,808 7,400 8,510 9,200 13,616 14,800 17,020

Collatz Trajectory (154 steps to reach 1)

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

680,800 340,400 170,200 85,100 42,550 21,275 63,826 31,913 95,740 47,870 23,935 71,806 35,903 107,710 53,855 161,566 80,783 242,350 121,175 363,526 181,763 545,290 272,645 817,936 408,968 204,484 102,242 51,121 153,364 76,682 38,341 115,024 57,512 28,756 14,378 7,189 21,568 10,784 5,392 2,696 1,348 674 337 1,012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1,456 728

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