λ
Prime Ledger

165,972

22 × 3 × 13831
Abundant Even Composite

165,972 has the prime decomposition 2^2 × 3 × 13831. Its 3 distinct prime factors produce 12 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 3 × 13831
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 12
Divisor Sum (σ) 387,296
Proper Divisor Sum 221,324
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #165961 ← → #165983

Radix Representation

Decimal 165972
Binary 101000100001010100 (18 bits)
Octal 0o504124
Hexadecimal 0x28854

Divisor Catalog (12)

1 2 3 4 6 12 13,831 27,662 41,493 55,324 82,986 165,972

Collatz Trajectory (46 steps to reach 1)

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

165,972 82,986 41,493 124,480 62,240 31,120 15,560 7,780 3,890 1,945 5,836 2,918 1,459 4,378 2,189 6,568 3,284 1,642 821 2,464 1,232 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

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