688,712

2³ × 19 × 23 × 197

688,712 factors as 2^3 × 19 × 23 × 197. Its 32 positive divisors give a proper-divisor sum of 736,888, so this integer is abundant. The Collatz stopping time is 110 steps.

Prime Factor Structure

Factorization String 2^3 × 19 × 23 × 197

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 1,425,600

Proper Divisor Sum 736,888

Digit Sum / Digital Root 32 (Root: 5)

Adjacent Primes #688697 ← → #688717

Radix Representation

Decimal	688712
Binary	10101000001001001000 (20 bits)
Octal	0o2501110
Hexadecimal	0xA8248

Divisor Catalog (32)

1 2 4 8 19 23 38 46 76 92 152 184 197 394 437 788 874 1,576 1,748 3,496 3,743 4,531 7,486 9,062 14,972 18,124 29,944 36,248 86,089 172,178 344,356 688,712

Collatz Trajectory (110 steps to reach 1)

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

688,712 344,356 172,178 86,089 258,268 129,134 64,567 193,702 96,851 290,554 145,277 435,832 217,916 108,958 54,479 163,438 81,719 245,158 122,579 367,738 183,869 551,608 275,804 137,902 68,951 206,854 103,427 310,282 155,141 465,424 232,712 116,356 58,178 29,089 87,268 43,634 21,817 65,452 32,726 16,363 49,090 24,545 73,636 36,818 18,409 55,228 27,614 13,807 41,422 20,711 62,134 31,067 93,202 46,601 139,804 69,902 34,951 104,854 52,427 157,282

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