7,789,628

2² × 7² × 11 × 3613

7,789,628 factors as 2^2 × 7^2 × 11 × 3613. Its 36 positive divisors give a proper-divisor sum of 9,514,204, so this integer is abundant. The Collatz stopping time is 173 steps.

Prime Factor Structure

Factorization String 2^2 × 7^2 × 11 × 3613

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 17,303,832

Proper Divisor Sum 9,514,204

Digit Sum / Digital Root 47 (Root: 2)

Adjacent Primes #7789627 ← → #7789657

Radix Representation

Decimal	7789628
Binary	11101101101110000111100 (23 bits)
Octal	0o35556074
Hexadecimal	0x76DC3C

Divisor Catalog (36)

Collatz Trajectory (173 steps to reach 1)

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

7,789,628 3,894,814 1,947,407 5,842,222 2,921,111 8,763,334 4,381,667 13,145,002 6,572,501 19,717,504 9,858,752 4,929,376 2,464,688 1,232,344 616,172 308,086 154,043 462,130 231,065 693,196 346,598 173,299 519,898 259,949 779,848 389,924 194,962 97,481 292,444 146,222 73,111 219,334 109,667 329,002 164,501 493,504 246,752 123,376 61,688 30,844 15,422 7,711 23,134 11,567 34,702 17,351 52,054 26,027 78,082 39,041 117,124 58,562 29,281 87,844 43,922 21,961 65,884 32,942 16,471 49,414

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