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Atlas › Integer Profiles › Node 77,251,160

77,251,160

23 × 5 × 7 × 275897
Abundant Even Composite

77,251,160 factors as 2^3 × 5 × 7 × 275897. Its 32 positive divisors give a proper-divisor sum of 121,395,400, so this integer is abundant. The Collatz stopping time is 122 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 7 × 275897
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 198,646,560
Proper Divisor Sum 121,395,400
Digit Sum / Digital Root 29 (Root: 2)
Adjacent Primes #77251159 ← → #77251183

Radix Representation

Decimal 77251160
Binary 100100110101100001001011000 (27 bits)
Octal 0o446541130
Hexadecimal 0x49AC258

Divisor Catalog (32)

1 2 4 5 7 8 10 14 20 28 35 40 56 70 140 280 275,897 551,794 1,103,588 1,379,485 1,931,279 2,207,176 2,758,970 3,862,558 5,517,940 7,725,116 9,656,395 11,035,880 15,450,232 19,312,790 38,625,580 77,251,160

Collatz Trajectory (122 steps to reach 1)

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

77,251,160 38,625,580 19,312,790 9,656,395 28,969,186 14,484,593 43,453,780 21,726,890 10,863,445 32,590,336 16,295,168 8,147,584 4,073,792 2,036,896 1,018,448 509,224 254,612 127,306 63,653 190,960 95,480 47,740 23,870 11,935 35,806 17,903 53,710 26,855 80,566 40,283 120,850 60,425 181,276 90,638 45,319 135,958 67,979 203,938 101,969 305,908 152,954 76,477 229,432 114,716 57,358 28,679 86,038 43,019 129,058 64,529 193,588 96,794 48,397 145,192 72,596 36,298 18,149 54,448 27,224 13,612

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