7,707,168

2⁵ × 3² × 7 × 3823

7,707,168 has the prime decomposition 2^5 × 3^2 × 7 × 3823. Its 4 distinct prime factors produce 72 positive divisors.

Prime Factor Structure

Factorization String 2^5 × 3^2 × 7 × 3823

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 25,054,848

Proper Divisor Sum 17,347,680

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #7707163 ← → #7707187

Radix Representation

Decimal	7707168
Binary	11101011001101000100000 (23 bits)
Octal	0o35315040
Hexadecimal	0x759A20

Divisor Catalog (60 of 72)

1 2 3 4 6 7 8 9 12 14 16 18 21 24 28 32 36 42 48 56 63 72 84 96 112 126 144 168 224 252 288 336 504 672 1,008 2,016 3,823 7,646 11,469 15,292 22,938 26,761 30,584 34,407 45,876 53,522 61,168 68,814 80,283 91,752 107,044 122,336 137,628 160,566 183,504 214,088 240,849 275,256 321,132 367,008

Collatz Trajectory (124 steps to reach 1)

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

7,707,168 3,853,584 1,926,792 963,396 481,698 240,849 722,548 361,274 180,637 541,912 270,956 135,478 67,739 203,218 101,609 304,828 152,414 76,207 228,622 114,311 342,934 171,467 514,402 257,201 771,604 385,802 192,901 578,704 289,352 144,676 72,338 36,169 108,508 54,254 27,127 81,382 40,691 122,074 61,037 183,112 91,556 45,778 22,889 68,668 34,334 17,167 51,502 25,751 77,254 38,627 115,882 57,941 173,824 86,912 43,456 21,728 10,864 5,432 2,716 1,358

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