228,288

2⁶ × 3 × 29 × 41

228,288 factors as 2^6 × 3 × 29 × 41. Its 56 positive divisors give a proper-divisor sum of 411,792, so this integer is abundant. The Collatz stopping time is 199 steps.

Prime Factor Structure

Factorization String 2^6 × 3 × 29 × 41

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 56

Divisor Sum (σ) 640,080

Proper Divisor Sum 411,792

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #228281 ← → #228299

Radix Representation

Decimal	228288
Binary	110111101111000000 (18 bits)
Octal	0o675700
Hexadecimal	0x37BC0

Divisor Catalog (56)

1 2 3 4 6 8 12 16 24 29 32 41 48 58 64 82 87 96 116 123 164 174 192 232 246 328 348 464 492 656 696 928 984 1,189 1,312 1,392 1,856 1,968 2,378 2,624 2,784 3,567 3,936 4,756 5,568 7,134 7,872 9,512 14,268 19,024 28,536 38,048 57,072 76,096 114,144 228,288

Collatz Trajectory (199 steps to reach 1)

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

228,288 114,144 57,072 28,536 14,268 7,134 3,567 10,702 5,351 16,054 8,027 24,082 12,041 36,124 18,062 9,031 27,094 13,547 40,642 20,321 60,964 30,482 15,241 45,724 22,862 11,431 34,294 17,147 51,442 25,721 77,164 38,582 19,291 57,874 28,937 86,812 43,406 21,703 65,110 32,555 97,666 48,833 146,500 73,250 36,625 109,876 54,938 27,469 82,408 41,204 20,602 10,301 30,904 15,452 7,726 3,863 11,590 5,795 17,386 8,693

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