684,012

2² × 3 × 7 × 17 × 479

684,012 factors as 2^2 × 3 × 7 × 17 × 479. Its 48 positive divisors give a proper-divisor sum of 1,251,348, so this integer is abundant. The Collatz stopping time is 335 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 7 × 17 × 479

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 1,935,360

Proper Divisor Sum 1,251,348

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #684007 ← → #684017

Radix Representation

Decimal	684012
Binary	10100110111111101100 (20 bits)
Octal	0o2467754
Hexadecimal	0xA6FEC

Divisor Catalog (48)

1 2 3 4 6 7 12 14 17 21 28 34 42 51 68 84 102 119 204 238 357 476 479 714 958 1,428 1,437 1,916 2,874 3,353 5,748 6,706 8,143 10,059 13,412 16,286 20,118 24,429 32,572 40,236 48,858 57,001 97,716 114,002 171,003 228,004 342,006 684,012

Collatz Trajectory (335 steps to reach 1)

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

684,012 342,006 171,003 513,010 256,505 769,516 384,758 192,379 577,138 288,569 865,708 432,854 216,427 649,282 324,641 973,924 486,962 243,481 730,444 365,222 182,611 547,834 273,917 821,752 410,876 205,438 102,719 308,158 154,079 462,238 231,119 693,358 346,679 1,040,038 520,019 1,560,058 780,029 2,340,088 1,170,044 585,022 292,511 877,534 438,767 1,316,302 658,151 1,974,454 987,227 2,961,682 1,480,841 4,442,524 2,221,262 1,110,631 3,331,894 1,665,947 4,997,842 2,498,921 7,496,764 3,748,382 1,874,191 5,622,574

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