89,316

2² × 3³ × 827

89,316 factors as 2^2 × 3^3 × 827. Its 24 positive divisors give a proper-divisor sum of 142,524, so this integer is abundant. The Collatz stopping time is 115 steps.

Prime Factor Structure

Factorization String 2^2 × 3^3 × 827

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 231,840

Proper Divisor Sum 142,524

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #89303 ← → #89317

Radix Representation

Decimal	89316
Binary	10101110011100100 (17 bits)
Octal	0o256344
Hexadecimal	0x15CE4

Divisor Catalog (24)

1 2 3 4 6 9 12 18 27 36 54 108 827 1,654 2,481 3,308 4,962 7,443 9,924 14,886 22,329 29,772 44,658 89,316

Collatz Trajectory (115 steps to reach 1)

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

89,316 44,658 22,329 66,988 33,494 16,747 50,242 25,121 75,364 37,682 18,841 56,524 28,262 14,131 42,394 21,197 63,592 31,796 15,898 7,949 23,848 11,924 5,962 2,981 8,944 4,472 2,236 1,118 559 1,678 839 2,518 1,259 3,778 1,889 5,668 2,834 1,417 4,252 2,126 1,063 3,190 1,595 4,786 2,393 7,180 3,590 1,795 5,386 2,693 8,080 4,040 2,020 1,010 505 1,516 758 379 1,138 569

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