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Atlas › Integer Profiles › Node 83,177,080

83,177,080

23 × 5 × 7 × 297061
Abundant Even Composite

83,177,080 factors as 2^3 × 5 × 7 × 297061. Its 32 positive divisors give a proper-divisor sum of 130,707,560, so this integer is abundant. The Collatz stopping time is 236 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 7 × 297061
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 213,884,640
Proper Divisor Sum 130,707,560
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #83177077 ← → #83177111

Radix Representation

Decimal 83177080
Binary 100111101010010111001111000 (27 bits)
Octal 0o475227170
Hexadecimal 0x4F52E78

Divisor Catalog (32)

1 2 4 5 7 8 10 14 20 28 35 40 56 70 140 280 297,061 594,122 1,188,244 1,485,305 2,079,427 2,376,488 2,970,610 4,158,854 5,941,220 8,317,708 10,397,135 11,882,440 16,635,416 20,794,270 41,588,540 83,177,080

Collatz Trajectory (236 steps to reach 1)

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

83,177,080 41,588,540 20,794,270 10,397,135 31,191,406 15,595,703 46,787,110 23,393,555 70,180,666 35,090,333 105,271,000 52,635,500 26,317,750 13,158,875 39,476,626 19,738,313 59,214,940 29,607,470 14,803,735 44,411,206 22,205,603 66,616,810 33,308,405 99,925,216 49,962,608 24,981,304 12,490,652 6,245,326 3,122,663 9,367,990 4,683,995 14,051,986 7,025,993 21,077,980 10,538,990 5,269,495 15,808,486 7,904,243 23,712,730 11,856,365 35,569,096 17,784,548 8,892,274 4,446,137 13,338,412 6,669,206 3,334,603 10,003,810 5,001,905 15,005,716 7,502,858 3,751,429 11,254,288 5,627,144 2,813,572 1,406,786 703,393 2,110,180 1,055,090 527,545

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