172,964

2² × 11 × 3931

172,964 factors as 2^2 × 11 × 3931. Its 12 positive divisors give a proper-divisor sum of 157,324, so this integer is deficient. The Collatz stopping time is 77 steps.

Prime Factor Structure

Factorization String 2^2 × 11 × 3931

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 330,288

Proper Divisor Sum 157,324

Digit Sum / Digital Root 29 (Root: 2)

Adjacent Primes #172933 ← → #172969

Radix Representation

Decimal	172964
Binary	101010001110100100 (18 bits)
Octal	0o521644
Hexadecimal	0x2A3A4

Divisor Catalog (12)

1 2 4 11 22 44 3,931 7,862 15,724 43,241 86,482 172,964

Collatz Trajectory (77 steps to reach 1)

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

172,964 86,482 43,241 129,724 64,862 32,431 97,294 48,647 145,942 72,971 218,914 109,457 328,372 164,186 82,093 246,280 123,140 61,570 30,785 92,356 46,178 23,089 69,268 34,634 17,317 51,952 25,976 12,988 6,494 3,247 9,742 4,871 14,614 7,307 21,922 10,961 32,884 16,442 8,221 24,664 12,332 6,166 3,083 9,250 4,625 13,876 6,938 3,469 10,408 5,204 2,602 1,301 3,904 1,952 976 488 244 122 61 184

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