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Atlas › Integer Profiles › Node 8,329,328

8,329,328

24 × 7 × 31 × 2399
Abundant Even Composite

8,329,328 factors as 2^4 × 7 × 31 × 2399. Its 40 positive divisors give a proper-divisor sum of 10,717,072, so this integer is abundant. The Collatz stopping time is 137 steps.

Prime Factor Structure

Factorization String 2^4 × 7 × 31 × 2399
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 19,046,400
Proper Divisor Sum 10,717,072
Digit Sum / Digital Root 35 (Root: 8)
Adjacent Primes #8329327 ← → #8329333

Radix Representation

Decimal 8329328
Binary 11111110001100001110000 (23 bits)
Octal 0o37614160
Hexadecimal 0x7F1870

Divisor Catalog (40)

1 2 4 7 8 14 16 28 31 56 62 112 124 217 248 434 496 868 1,736 2,399 3,472 4,798 9,596 16,793 19,192 33,586 38,384 67,172 74,369 134,344 148,738 268,688 297,476 520,583 594,952 1,041,166 1,189,904 2,082,332 4,164,664 8,329,328

Collatz Trajectory (137 steps to reach 1)

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

8,329,328 4,164,664 2,082,332 1,041,166 520,583 1,561,750 780,875 2,342,626 1,171,313 3,513,940 1,756,970 878,485 2,635,456 1,317,728 658,864 329,432 164,716 82,358 41,179 123,538 61,769 185,308 92,654 46,327 138,982 69,491 208,474 104,237 312,712 156,356 78,178 39,089 117,268 58,634 29,317 87,952 43,976 21,988 10,994 5,497 16,492 8,246 4,123 12,370 6,185 18,556 9,278 4,639 13,918 6,959 20,878 10,439 31,318 15,659 46,978 23,489 70,468 35,234 17,617 52,852

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