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832,384

27 × 7 × 929
Abundant Even Composite

832,384 factors as 2^7 × 7 × 929. Its 32 positive divisors give a proper-divisor sum of 1,064,816, so this integer is abundant. The Collatz stopping time is 69 steps.

Prime Factor Structure

Factorization String 2^7 × 7 × 929
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 1,897,200
Proper Divisor Sum 1,064,816
Digit Sum / Digital Root 28 (Root: 1)
Adjacent Primes #832379 ← → #832399

Radix Representation

Decimal 832384
Binary 11001011001110000000 (20 bits)
Octal 0o3131600
Hexadecimal 0xCB380

Divisor Catalog (32)

1 2 4 7 8 14 16 28 32 56 64 112 128 224 448 896 929 1,858 3,716 6,503 7,432 13,006 14,864 26,012 29,728 52,024 59,456 104,048 118,912 208,096 416,192 832,384

Collatz Trajectory (69 steps to reach 1)

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

832,384 416,192 208,096 104,048 52,024 26,012 13,006 6,503 19,510 9,755 29,266 14,633 43,900 21,950 10,975 32,926 16,463 49,390 24,695 74,086 37,043 111,130 55,565 166,696 83,348 41,674 20,837 62,512 31,256 15,628 7,814 3,907 11,722 5,861 17,584 8,792 4,396 2,198 1,099 3,298 1,649 4,948 2,474 1,237 3,712 1,856 928 464 232 116 58 29 88 44 22 11 34 17 52 26

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