48,654

2 × 3³ × 17 × 53

Starting at 48,654, the Collatz iteration reaches 1 after 65 steps. The first transition is 24327; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2 × 3^3 × 17 × 53

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 116,640

Proper Divisor Sum 67,986

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #48649 ← → #48661

Radix Representation

Decimal	48654
Binary	1011111000001110 (16 bits)
Octal	0o137016
Hexadecimal	0xBE0E

Divisor Catalog (32)

1 2 3 6 9 17 18 27 34 51 53 54 102 106 153 159 306 318 459 477 901 918 954 1,431 1,802 2,703 2,862 5,406 8,109 16,218 24,327 48,654

Collatz Trajectory (65 steps to reach 1)

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

48,654 24,327 72,982 36,491 109,474 54,737 164,212 82,106 41,053 123,160 61,580 30,790 15,395 46,186 23,093 69,280 34,640 17,320 8,660 4,330 2,165 6,496 3,248 1,624 812 406 203 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10

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