λ
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315,432

23 × 32 × 13 × 337
Abundant Even Composite

315,432 factors as 2^3 × 3^2 × 13 × 337. Its 48 positive divisors give a proper-divisor sum of 607,308, so this integer is abundant. The Collatz stopping time is 65 steps.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 13 × 337
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 922,740
Proper Divisor Sum 607,308
Digit Sum / Digital Root 18 (Root: 9)
Adjacent Primes #315421 ← → #315437

Radix Representation

Decimal 315432
Binary 1001101000000101000 (19 bits)
Octal 0o1150050
Hexadecimal 0x4D028

Divisor Catalog (48)

1 2 3 4 6 8 9 12 13 18 24 26 36 39 52 72 78 104 117 156 234 312 337 468 674 936 1,011 1,348 2,022 2,696 3,033 4,044 4,381 6,066 8,088 8,762 12,132 13,143 17,524 24,264 26,286 35,048 39,429 52,572 78,858 105,144 157,716 315,432

Collatz Trajectory (65 steps to reach 1)

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

315,432 157,716 78,858 39,429 118,288 59,144 29,572 14,786 7,393 22,180 11,090 5,545 16,636 8,318 4,159 12,478 6,239 18,718 9,359 28,078 14,039 42,118 21,059 63,178 31,589 94,768 47,384 23,692 11,846 5,923 17,770 8,885 26,656 13,328 6,664 3,332 1,666 833 2,500 1,250 625 1,876 938 469 1,408 704 352 176 88 44 22 11 34 17 52 26 13 40 20 10

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