10,002,825

3³ × 5² × 7 × 29 × 73

10,002,825 factors as 3^3 × 5^2 × 7 × 29 × 73. Its 96 positive divisors give a proper-divisor sum of 12,019,575, so this integer is abundant. The Collatz stopping time is 189 steps.

Prime Factor Structure

Factorization String 3^3 × 5^2 × 7 × 29 × 73

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 22,022,400

Proper Divisor Sum 12,019,575

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #10002823 ← → #10002829

Radix Representation

Decimal	10002825
Binary	100110001010000110001001 (24 bits)
Octal	0o46120611
Hexadecimal	0x98A189

Divisor Catalog (60 of 96)

1 3 5 7 9 15 21 25 27 29 35 45 63 73 75 87 105 135 145 175 189 203 219 225 261 315 365 435 511 525 609 657 675 725 783 945 1,015 1,095 1,305 1,533 1,575 1,825 1,827 1,971 2,117 2,175 2,555 3,045 3,285 3,915 4,599 4,725 5,075 5,475 5,481 6,351 6,525 7,665 9,135 9,855

Collatz Trajectory (189 steps to reach 1)

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

10,002,825 30,008,476 15,004,238 7,502,119 22,506,358 11,253,179 33,759,538 16,879,769 50,639,308 25,319,654 12,659,827 37,979,482 18,989,741 56,969,224 28,484,612 14,242,306 7,121,153 21,363,460 10,681,730 5,340,865 16,022,596 8,011,298 4,005,649 12,016,948 6,008,474 3,004,237 9,012,712 4,506,356 2,253,178 1,126,589 3,379,768 1,689,884 844,942 422,471 1,267,414 633,707 1,901,122 950,561 2,851,684 1,425,842 712,921 2,138,764 1,069,382 534,691 1,604,074 802,037 2,406,112 1,203,056 601,528 300,764 150,382 75,191 225,574 112,787 338,362 169,181 507,544 253,772 126,886 63,443

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