828,625

5³ × 7 × 947

Starting at 828,625, the Collatz iteration reaches 1 after 175 steps. The first transition is 2485876; the starting value is odd with 16 positive divisors.

Prime Factor Structure

Factorization String 5^3 × 7 × 947

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 1,183,104

Proper Divisor Sum 354,479

Digit Sum / Digital Root 31 (Root: 4)

Adjacent Primes #828601 ← → #828637

Radix Representation

Decimal	828625
Binary	11001010010011010001 (20 bits)
Octal	0o3122321
Hexadecimal	0xCA4D1

Divisor Catalog (16)

1 5 7 25 35 125 175 875 947 4,735 6,629 23,675 33,145 118,375 165,725 828,625

Collatz Trajectory (175 steps to reach 1)

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

828,625 2,485,876 1,242,938 621,469 1,864,408 932,204 466,102 233,051 699,154 349,577 1,048,732 524,366 262,183 786,550 393,275 1,179,826 589,913 1,769,740 884,870 442,435 1,327,306 663,653 1,990,960 995,480 497,740 248,870 124,435 373,306 186,653 559,960 279,980 139,990 69,995 209,986 104,993 314,980 157,490 78,745 236,236 118,118 59,059 177,178 88,589 265,768 132,884 66,442 33,221 99,664 49,832 24,916 12,458 6,229 18,688 9,344 4,672 2,336 1,168 584 292 146

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