252,824

2³ × 11 × 13² × 17

Starting at 252,824, the Collatz iteration reaches 1 after 44 steps. The first transition is 126412; the starting value is even with 48 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 11 × 13^2 × 17

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 592,920

Proper Divisor Sum 340,096

Digit Sum / Digital Root 23 (Root: 5)

Adjacent Primes #252823 ← → #252827

Radix Representation

Decimal	252824
Binary	111101101110011000 (18 bits)
Octal	0o755630
Hexadecimal	0x3DB98

Divisor Catalog (48)

1 2 4 8 11 13 17 22 26 34 44 52 68 88 104 136 143 169 187 221 286 338 374 442 572 676 748 884 1,144 1,352 1,496 1,768 1,859 2,431 2,873 3,718 4,862 5,746 7,436 9,724 11,492 14,872 19,448 22,984 31,603 63,206 126,412 252,824

Collatz Trajectory (44 steps to reach 1)

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

252,824 126,412 63,206 31,603 94,810 47,405 142,216 71,108 35,554 17,777 53,332 26,666 13,333 40,000 20,000 10,000 5,000 2,500 1,250 625 1,876 938 469 1,408 704 352 176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

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