λ
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684,384

25 × 3 × 7129
Abundant Even Composite

684,384 factors as 2^5 × 3 × 7129. Its 24 positive divisors give a proper-divisor sum of 1,112,376, so this integer is abundant. The Collatz stopping time is 167 steps.

Prime Factor Structure

Factorization String 2^5 × 3 × 7129
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 1,796,760
Proper Divisor Sum 1,112,376
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #684379 ← → #684407

Radix Representation

Decimal 684384
Binary 10100111000101100000 (20 bits)
Octal 0o2470540
Hexadecimal 0xA7160

Divisor Catalog (24)

1 2 3 4 6 8 12 16 24 32 48 96 7,129 14,258 21,387 28,516 42,774 57,032 85,548 114,064 171,096 228,128 342,192 684,384

Collatz Trajectory (167 steps to reach 1)

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

684,384 342,192 171,096 85,548 42,774 21,387 64,162 32,081 96,244 48,122 24,061 72,184 36,092 18,046 9,023 27,070 13,535 40,606 20,303 60,910 30,455 91,366 45,683 137,050 68,525 205,576 102,788 51,394 25,697 77,092 38,546 19,273 57,820 28,910 14,455 43,366 21,683 65,050 32,525 97,576 48,788 24,394 12,197 36,592 18,296 9,148 4,574 2,287 6,862 3,431 10,294 5,147 15,442 7,721 23,164 11,582 5,791 17,374 8,687 26,062

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