λ
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689,376

25 × 3 × 43 × 167
Abundant Even Composite

689,376 factors as 2^5 × 3 × 43 × 167. Its 48 positive divisors give a proper-divisor sum of 1,173,408, so this integer is abundant. The Collatz stopping time is 79 steps.

Prime Factor Structure

Factorization String 2^5 × 3 × 43 × 167
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 1,862,784
Proper Divisor Sum 1,173,408
Digit Sum / Digital Root 39 (Root: 3)
Adjacent Primes #689369 ← → #689383

Radix Representation

Decimal 689376
Binary 10101000010011100000 (20 bits)
Octal 0o2502340
Hexadecimal 0xA84E0

Divisor Catalog (48)

1 2 3 4 6 8 12 16 24 32 43 48 86 96 129 167 172 258 334 344 501 516 668 688 1,002 1,032 1,336 1,376 2,004 2,064 2,672 4,008 4,128 5,344 7,181 8,016 14,362 16,032 21,543 28,724 43,086 57,448 86,172 114,896 172,344 229,792 344,688 689,376

Collatz Trajectory (79 steps to reach 1)

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

689,376 344,688 172,344 86,172 43,086 21,543 64,630 32,315 96,946 48,473 145,420 72,710 36,355 109,066 54,533 163,600 81,800 40,900 20,450 10,225 30,676 15,338 7,669 23,008 11,504 5,752 2,876 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 1,300 650 325 976 488 244 122

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