504,448

2⁷ × 7 × 563

Starting at 504,448, the Collatz iteration reaches 1 after 32 steps. The first transition is 252224; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2^7 × 7 × 563

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 1,150,560

Proper Divisor Sum 646,112

Digit Sum / Digital Root 25 (Root: 7)

Adjacent Primes #504403 ← → #504457

Radix Representation

Decimal	504448
Binary	1111011001010000000 (19 bits)
Octal	0o1731200
Hexadecimal	0x7B280

Divisor Catalog (32)

1 2 4 7 8 14 16 28 32 56 64 112 128 224 448 563 896 1,126 2,252 3,941 4,504 7,882 9,008 15,764 18,016 31,528 36,032 63,056 72,064 126,112 252,224 504,448

Collatz Trajectory (32 steps to reach 1)

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

504,448 252,224 126,112 63,056 31,528 15,764 7,882 3,941 11,824 5,912 2,956 1,478 739 2,218 1,109 3,328 1,664 832 416 208 104 52 26 13 40 20 10 5 16 8 4 2 1

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