72,216

2³ × 3² × 17 × 59

72,216 factors as 2^3 × 3^2 × 17 × 59. Its 48 positive divisors give a proper-divisor sum of 138,384, so this integer is abundant. The Collatz stopping time is 187 steps.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 17 × 59

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 210,600

Proper Divisor Sum 138,384

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #72211 ← → #72221

Radix Representation

Decimal	72216
Binary	10001101000011000 (17 bits)
Octal	0o215030
Hexadecimal	0x11A18

Divisor Catalog (48)

1 2 3 4 6 8 9 12 17 18 24 34 36 51 59 68 72 102 118 136 153 177 204 236 306 354 408 472 531 612 708 1,003 1,062 1,224 1,416 2,006 2,124 3,009 4,012 4,248 6,018 8,024 9,027 12,036 18,054 24,072 36,108 72,216

Collatz Trajectory (187 steps to reach 1)

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

72,216 36,108 18,054 9,027 27,082 13,541 40,624 20,312 10,156 5,078 2,539 7,618 3,809 11,428 5,714 2,857 8,572 4,286 2,143 6,430 3,215 9,646 4,823 14,470 7,235 21,706 10,853 32,560 16,280 8,140 4,070 2,035 6,106 3,053 9,160 4,580 2,290 1,145 3,436 1,718 859 2,578 1,289 3,868 1,934 967 2,902 1,451 4,354 2,177 6,532 3,266 1,633 4,900 2,450 1,225 3,676 1,838 919 2,758

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