257,872

2⁴ × 71 × 227

Starting at 257,872, the Collatz iteration reaches 1 after 101 steps. The first transition is 128936; the starting value is even with 20 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 71 × 227

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 20

Divisor Sum (σ) 508,896

Proper Divisor Sum 251,024

Digit Sum / Digital Root 31 (Root: 4)

Adjacent Primes #257869 ← → #257879

Radix Representation

Decimal	257872
Binary	111110111101010000 (18 bits)
Octal	0o767520
Hexadecimal	0x3EF50

Divisor Catalog (20)

1 2 4 8 16 71 142 227 284 454 568 908 1,136 1,816 3,632 16,117 32,234 64,468 128,936 257,872

Collatz Trajectory (101 steps to reach 1)

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

257,872 128,936 64,468 32,234 16,117 48,352 24,176 12,088 6,044 3,022 1,511 4,534 2,267 6,802 3,401 10,204 5,102 2,551 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 19,682 9,841

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