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Atlas › Integer Profiles › Node 80,960,964

80,960,964

22 × 3 × 7 × 31 × 31091
Abundant Even Composite

80,960,964 factors as 2^2 × 3 × 7 × 31 × 31091. Its 48 positive divisors give a proper-divisor sum of 141,906,492, so this integer is abundant. The Collatz stopping time is 109 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 7 × 31 × 31091
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 222,867,456
Proper Divisor Sum 141,906,492
Digit Sum / Digital Root 42 (Root: 6)
Adjacent Primes #80960963 ← → #80960981

Radix Representation

Decimal 80960964
Binary 100110100110101110111000100 (27 bits)
Octal 0o464656704
Hexadecimal 0x4D35DC4

Divisor Catalog (48)

1 2 3 4 6 7 12 14 21 28 31 42 62 84 93 124 186 217 372 434 651 868 1,302 2,604 31,091 62,182 93,273 124,364 186,546 217,637 373,092 435,274 652,911 870,548 963,821 1,305,822 1,927,642 2,611,644 2,891,463 3,855,284 5,782,926 6,746,747 11,565,852 13,493,494 20,240,241 26,986,988 40,480,482 80,960,964

Collatz Trajectory (109 steps to reach 1)

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

80,960,964 40,480,482 20,240,241 60,720,724 30,360,362 15,180,181 45,540,544 22,770,272 11,385,136 5,692,568 2,846,284 1,423,142 711,571 2,134,714 1,067,357 3,202,072 1,601,036 800,518 400,259 1,200,778 600,389 1,801,168 900,584 450,292 225,146 112,573 337,720 168,860 84,430 42,215 126,646 63,323 189,970 94,985 284,956 142,478 71,239 213,718 106,859 320,578 160,289 480,868 240,434 120,217 360,652 180,326 90,163 270,490 135,245 405,736 202,868 101,434 50,717 152,152 76,076 38,038 19,019 57,058 28,529 85,588

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