642,912

2⁵ × 3 × 37 × 181

642,912 factors as 2^5 × 3 × 37 × 181. Its 48 positive divisors give a proper-divisor sum of 1,099,920, so this integer is abundant. The Collatz stopping time is 48 steps.

Prime Factor Structure

Factorization String 2^5 × 3 × 37 × 181

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 1,742,832

Proper Divisor Sum 1,099,920

Digit Sum / Digital Root 24 (Root: 6)

Adjacent Primes #642907 ← → #642931

Radix Representation

Decimal	642912
Binary	10011100111101100000 (20 bits)
Octal	0o2347540
Hexadecimal	0x9CF60

Divisor Catalog (48)

1 2 3 4 6 8 12 16 24 32 37 48 74 96 111 148 181 222 296 362 444 543 592 724 888 1,086 1,184 1,448 1,776 2,172 2,896 3,552 4,344 5,792 6,697 8,688 13,394 17,376 20,091 26,788 40,182 53,576 80,364 107,152 160,728 214,304 321,456 642,912

Collatz Trajectory (48 steps to reach 1)

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

642,912 321,456 160,728 80,364 40,182 20,091 60,274 30,137 90,412 45,206 22,603 67,810 33,905 101,716 50,858 25,429 76,288 38,144 19,072 9,536 4,768 2,384 1,192 596 298 149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

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