653,604

2² × 3 × 7 × 31 × 251

653,604 factors as 2^2 × 3 × 7 × 31 × 251. Its 48 positive divisors give a proper-divisor sum of 1,152,732, so this integer is abundant. The Collatz stopping time is 154 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 7 × 31 × 251

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 1,806,336

Proper Divisor Sum 1,152,732

Digit Sum / Digital Root 24 (Root: 6)

Adjacent Primes #653593 ← → #653617

Radix Representation

Decimal	653604
Binary	10011111100100100100 (20 bits)
Octal	0o2374444
Hexadecimal	0x9F924

Divisor Catalog (48)

1 2 3 4 6 7 12 14 21 28 31 42 62 84 93 124 186 217 251 372 434 502 651 753 868 1,004 1,302 1,506 1,757 2,604 3,012 3,514 5,271 7,028 7,781 10,542 15,562 21,084 23,343 31,124 46,686 54,467 93,372 108,934 163,401 217,868 326,802 653,604

Collatz Trajectory (154 steps to reach 1)

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

653,604 326,802 163,401 490,204 245,102 122,551 367,654 183,827 551,482 275,741 827,224 413,612 206,806 103,403 310,210 155,105 465,316 232,658 116,329 348,988 174,494 87,247 261,742 130,871 392,614 196,307 588,922 294,461 883,384 441,692 220,846 110,423 331,270 165,635 496,906 248,453 745,360 372,680 186,340 93,170 46,585 139,756 69,878 34,939 104,818 52,409 157,228 78,614 39,307 117,922 58,961 176,884 88,442 44,221 132,664 66,332 33,166 16,583 49,750 24,875

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