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Atlas › Integer Profiles › Node 71,335,840

71,335,840

25 × 5 × 61 × 7309
Abundant Even Composite

71,335,840 factors as 2^5 × 5 × 61 × 7309. Its 48 positive divisors give a proper-divisor sum of 99,981,320, so this integer is abundant. The Collatz stopping time is 166 steps.

Prime Factor Structure

Factorization String 2^5 × 5 × 61 × 7309
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 171,317,160
Proper Divisor Sum 99,981,320
Digit Sum / Digital Root 31 (Root: 4)
Adjacent Primes #71335829 ← → #71335871

Radix Representation

Decimal 71335840
Binary 100010000000111111110100000 (27 bits)
Octal 0o420077640
Hexadecimal 0x4407FA0

Divisor Catalog (48)

1 2 4 5 8 10 16 20 32 40 61 80 122 160 244 305 488 610 976 1,220 1,952 2,440 4,880 7,309 9,760 14,618 29,236 36,545 58,472 73,090 116,944 146,180 233,888 292,360 445,849 584,720 891,698 1,169,440 1,783,396 2,229,245 3,566,792 4,458,490 7,133,584 8,916,980 14,267,168 17,833,960 35,667,920 71,335,840

Collatz Trajectory (166 steps to reach 1)

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

71,335,840 35,667,920 17,833,960 8,916,980 4,458,490 2,229,245 6,687,736 3,343,868 1,671,934 835,967 2,507,902 1,253,951 3,761,854 1,880,927 5,642,782 2,821,391 8,464,174 4,232,087 12,696,262 6,348,131 19,044,394 9,522,197 28,566,592 14,283,296 7,141,648 3,570,824 1,785,412 892,706 446,353 1,339,060 669,530 334,765 1,004,296 502,148 251,074 125,537 376,612 188,306 94,153 282,460 141,230 70,615 211,846 105,923 317,770 158,885 476,656 238,328 119,164 59,582 29,791 89,374 44,687 134,062 67,031 201,094 100,547 301,642 150,821 452,464

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