101,964

2² × 3 × 29 × 293

101,964 factors as 2^2 × 3 × 29 × 293. Its 24 positive divisors give a proper-divisor sum of 144,996, so this integer is abundant. The Collatz stopping time is 84 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 29 × 293

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 246,960

Proper Divisor Sum 144,996

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #101963 ← → #101977

Radix Representation

Decimal	101964
Binary	11000111001001100 (17 bits)
Octal	0o307114
Hexadecimal	0x18E4C

Divisor Catalog (24)

1 2 3 4 6 12 29 58 87 116 174 293 348 586 879 1,172 1,758 3,516 8,497 16,994 25,491 33,988 50,982 101,964

Collatz Trajectory (84 steps to reach 1)

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

101,964 50,982 25,491 76,474 38,237 114,712 57,356 28,678 14,339 43,018 21,509 64,528 32,264 16,132 8,066 4,033 12,100 6,050 3,025 9,076 4,538 2,269 6,808 3,404 1,702 851 2,554 1,277 3,832 1,916 958 479 1,438 719 2,158 1,079 3,238 1,619 4,858 2,429 7,288 3,644 1,822 911 2,734 1,367 4,102 2,051 6,154 3,077 9,232 4,616 2,308 1,154 577 1,732 866 433 1,300 650

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