677,964

2² × 3 × 7² × 1153

677,964 factors as 2^2 × 3 × 7^2 × 1153. Its 36 positive divisors give a proper-divisor sum of 1,163,820, so this integer is abundant. The Collatz stopping time is 110 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 7^2 × 1153

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 1,841,784

Proper Divisor Sum 1,163,820

Digit Sum / Digital Root 39 (Root: 3)

Adjacent Primes #677959 ← → #677983

Radix Representation

Decimal	677964
Binary	10100101100001001100 (20 bits)
Octal	0o2454114
Hexadecimal	0xA584C

Divisor Catalog (36)

Collatz Trajectory (110 steps to reach 1)

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

677,964 338,982 169,491 508,474 254,237 762,712 381,356 190,678 95,339 286,018 143,009 429,028 214,514 107,257 321,772 160,886 80,443 241,330 120,665 361,996 180,998 90,499 271,498 135,749 407,248 203,624 101,812 50,906 25,453 76,360 38,180 19,090 9,545 28,636 14,318 7,159 21,478 10,739 32,218 16,109 48,328 24,164 12,082 6,041 18,124 9,062 4,531 13,594 6,797 20,392 10,196 5,098 2,549 7,648 3,824 1,912 956 478 239 718

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