171,972

2² × 3² × 17 × 281

171,972 has digital root 9. The neighboring primes are 171947 and 172001; its proper-divisor sum differs from the starting integer by 117,972.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 17 × 281

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 461,916

Proper Divisor Sum 289,944

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #171947 ← → #172001

Radix Representation

Decimal	171972
Binary	101001111111000100 (18 bits)
Octal	0o517704
Hexadecimal	0x29FC4

Divisor Catalog (36)

1 2 3 4 6 9 12 17 18 34 36 51 68 102 153 204 281 306 562 612 843 1,124 1,686 2,529 3,372 4,777 5,058 9,554 10,116 14,331 19,108 28,662 42,993 57,324 85,986 171,972

Collatz Trajectory (103 steps to reach 1)

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

171,972 85,986 42,993 128,980 64,490 32,245 96,736 48,368 24,184 12,092 6,046 3,023 9,070 4,535 13,606 6,803 20,410 10,205 30,616 15,308 7,654 3,827 11,482 5,741 17,224 8,612 4,306 2,153 6,460 3,230 1,615 4,846 2,423 7,270 3,635 10,906 5,453 16,360 8,180 4,090 2,045 6,136 3,068 1,534 767 2,302 1,151 3,454 1,727 5,182 2,591 7,774 3,887 11,662 5,831 17,494 8,747 26,242 13,121 39,364

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