7,829,874

2 × 3² × 13 × 33461

7,829,874 factors as 2 × 3^2 × 13 × 33461. Its 24 positive divisors give a proper-divisor sum of 10,440,378, so this integer is abundant. The Collatz stopping time is 199 steps.

Prime Factor Structure

Factorization String 2 × 3^2 × 13 × 33461

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 18,270,252

Proper Divisor Sum 10,440,378

Digit Sum / Digital Root 45 (Root: 9)

Adjacent Primes #7829873 ← → #7829917

Radix Representation

Decimal	7829874
Binary	11101110111100101110010 (23 bits)
Octal	0o35674562
Hexadecimal	0x777972

Divisor Catalog (24)

Collatz Trajectory (199 steps to reach 1)

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

7,829,874 3,914,937 11,744,812 5,872,406 2,936,203 8,808,610 4,404,305 13,212,916 6,606,458 3,303,229 9,909,688 4,954,844 2,477,422 1,238,711 3,716,134 1,858,067 5,574,202 2,787,101 8,361,304 4,180,652 2,090,326 1,045,163 3,135,490 1,567,745 4,703,236 2,351,618 1,175,809 3,527,428 1,763,714 881,857 2,645,572 1,322,786 661,393 1,984,180 992,090 496,045 1,488,136 744,068 372,034 186,017 558,052 279,026 139,513 418,540 209,270 104,635 313,906 156,953 470,860 235,430 117,715 353,146 176,573 529,720 264,860 132,430 66,215 198,646 99,323 297,970

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