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9,727,728

24 × 3 × 202661
Abundant Even Composite

9,727,728 factors as 2^4 × 3 × 202661. Its 20 positive divisors give a proper-divisor sum of 15,402,360, so this integer is abundant. The Collatz stopping time is 119 steps.

Prime Factor Structure

Factorization String 2^4 × 3 × 202661
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 20
Divisor Sum (σ) 25,130,088
Proper Divisor Sum 15,402,360
Digit Sum / Digital Root 42 (Root: 6)
Adjacent Primes #9727709 ← → #9727747

Radix Representation

Decimal 9727728
Binary 100101000110111011110000 (24 bits)
Octal 0o45067360
Hexadecimal 0x946EF0

Divisor Catalog (20)

1 2 3 4 6 8 12 16 24 48 202,661 405,322 607,983 810,644 1,215,966 1,621,288 2,431,932 3,242,576 4,863,864 9,727,728

Collatz Trajectory (119 steps to reach 1)

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

9,727,728 4,863,864 2,431,932 1,215,966 607,983 1,823,950 911,975 2,735,926 1,367,963 4,103,890 2,051,945 6,155,836 3,077,918 1,538,959 4,616,878 2,308,439 6,925,318 3,462,659 10,387,978 5,193,989 15,581,968 7,790,984 3,895,492 1,947,746 973,873 2,921,620 1,460,810 730,405 2,191,216 1,095,608 547,804 273,902 136,951 410,854 205,427 616,282 308,141 924,424 462,212 231,106 115,553 346,660 173,330 86,665 259,996 129,998 64,999 194,998 97,499 292,498 146,249 438,748 219,374 109,687 329,062 164,531 493,594 246,797 740,392 370,196

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