167,948

2² × 11² × 347

167,948 factors as 2^2 × 11^2 × 347. Its 18 positive divisors give a proper-divisor sum of 156,040, so this integer is deficient. The Collatz stopping time is 121 steps.

Prime Factor Structure

Factorization String 2^2 × 11^2 × 347

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 18

Divisor Sum (σ) 323,988

Proper Divisor Sum 156,040

Digit Sum / Digital Root 35 (Root: 8)

Adjacent Primes #167917 ← → #167953

Radix Representation

Decimal	167948
Binary	101001000000001100 (18 bits)
Octal	0o510014
Hexadecimal	0x2900C

Divisor Catalog (18)

1 2 4 11 22 44 121 242 347 484 694 1,388 3,817 7,634 15,268 41,987 83,974 167,948

Collatz Trajectory (121 steps to reach 1)

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

167,948 83,974 41,987 125,962 62,981 188,944 94,472 47,236 23,618 11,809 35,428 17,714 8,857 26,572 13,286 6,643 19,930 9,965 29,896 14,948 7,474 3,737 11,212 5,606 2,803 8,410 4,205 12,616 6,308 3,154 1,577 4,732 2,366 1,183 3,550 1,775 5,326 2,663 7,990 3,995 11,986 5,993 17,980 8,990 4,495 13,486 6,743 20,230 10,115 30,346 15,173 45,520 22,760 11,380 5,690 2,845 8,536 4,268 2,134 1,067

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