837,564

2² × 3 × 7 × 13² × 59

837,564 factors as 2^2 × 3 × 7 × 13^2 × 59. Its 72 positive divisors give a proper-divisor sum of 1,621,956, so this integer is abundant. The Collatz stopping time is 113 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 7 × 13^2 × 59

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 2,459,520

Proper Divisor Sum 1,621,956

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #837533 ← → #837583

Radix Representation

Decimal	837564
Binary	11001100011110111100 (20 bits)
Octal	0o3143674
Hexadecimal	0xCC7BC

Divisor Catalog (60 of 72)

1 2 3 4 6 7 12 13 14 21 26 28 39 42 52 59 78 84 91 118 156 169 177 182 236 273 338 354 364 413 507 546 676 708 767 826 1,014 1,092 1,183 1,239 1,534 1,652 2,028 2,301 2,366 2,478 3,068 3,549 4,602 4,732 4,956 5,369 7,098 9,204 9,971 10,738 14,196 16,107 19,942 21,476

Collatz Trajectory (113 steps to reach 1)

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

837,564 418,782 209,391 628,174 314,087 942,262 471,131 1,413,394 706,697 2,120,092 1,060,046 530,023 1,590,070 795,035 2,385,106 1,192,553 3,577,660 1,788,830 894,415 2,683,246 1,341,623 4,024,870 2,012,435 6,037,306 3,018,653 9,055,960 4,527,980 2,263,990 1,131,995 3,395,986 1,697,993 5,093,980 2,546,990 1,273,495 3,820,486 1,910,243 5,730,730 2,865,365 8,596,096 4,298,048 2,149,024 1,074,512 537,256 268,628 134,314 67,157 201,472 100,736 50,368 25,184 12,592 6,296 3,148 1,574 787 2,362 1,181 3,544 1,772 886

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