101,748

2² × 3 × 61 × 139

Starting at 101,748, the Collatz iteration reaches 1 after 84 steps. The first transition is 50874; the starting value is even with 24 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 3 × 61 × 139

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 243,040

Proper Divisor Sum 141,292

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #101747 ← → #101749

Radix Representation

Decimal	101748
Binary	11000110101110100 (17 bits)
Octal	0o306564
Hexadecimal	0x18D74

Divisor Catalog (24)

1 2 3 4 6 12 61 122 139 183 244 278 366 417 556 732 834 1,668 8,479 16,958 25,437 33,916 50,874 101,748

Collatz Trajectory (84 steps to reach 1)

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

101,748 50,874 25,437 76,312 38,156 19,078 9,539 28,618 14,309 42,928 21,464 10,732 5,366 2,683 8,050 4,025 12,076 6,038 3,019 9,058 4,529 13,588 6,794 3,397 10,192 5,096 2,548 1,274 637 1,912 956 478 239 718 359 1,078 539 1,618 809 2,428 1,214 607 1,822 911 2,734 1,367 4,102 2,051 6,154 3,077 9,232 4,616 2,308 1,154 577 1,732 866 433 1,300 650

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