40,638

2 × 3 × 13 × 521

40,638 factors as 2 × 3 × 13 × 521. Its 16 positive divisors give a proper-divisor sum of 47,058, so this integer is abundant. The Collatz stopping time is 181 steps.

Prime Factor Structure

Factorization String 2 × 3 × 13 × 521

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 87,696

Proper Divisor Sum 47,058

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #40637 ← → #40639

Radix Representation

Decimal	40638
Binary	1001111010111110 (16 bits)
Octal	0o117276
Hexadecimal	0x9EBE

Divisor Catalog (16)

1 2 3 6 13 26 39 78 521 1,042 1,563 3,126 6,773 13,546 20,319 40,638

Collatz Trajectory (181 steps to reach 1)

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

40,638 20,319 60,958 30,479 91,438 45,719 137,158 68,579 205,738 102,869 308,608 154,304 77,152 38,576 19,288 9,644 4,822 2,411 7,234 3,617 10,852 5,426 2,713 8,140 4,070 2,035 6,106 3,053 9,160 4,580 2,290 1,145 3,436 1,718 859 2,578 1,289 3,868 1,934 967 2,902 1,451 4,354 2,177 6,532 3,266 1,633 4,900 2,450 1,225 3,676 1,838 919 2,758 1,379 4,138 2,069 6,208 3,104 1,552

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