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Atlas › Integer Profiles › Node 76,042,960

76,042,960

24 × 5 × 7 × 251 × 541
Abundant Even Composite

76,042,960 factors as 2^4 × 5 × 7 × 251 × 541. Its 80 positive divisors give a proper-divisor sum of 127,194,032, so this integer is abundant. The Collatz stopping time is 78 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 7 × 251 × 541
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 80
Divisor Sum (σ) 203,236,992
Proper Divisor Sum 127,194,032
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #76042933 ← → #76042961

Radix Representation

Decimal 76042960
Binary 100100010000101001011010000 (27 bits)
Octal 0o442051320
Hexadecimal 0x48852D0

Divisor Catalog (60 of 80)

1 2 4 5 7 8 10 14 16 20 28 35 40 56 70 80 112 140 251 280 502 541 560 1,004 1,082 1,255 1,757 2,008 2,164 2,510 2,705 3,514 3,787 4,016 4,328 5,020 5,410 7,028 7,574 8,656 8,785 10,040 10,820 14,056 15,148 17,570 18,935 20,080 21,640 28,112 30,296 35,140 37,870 43,280 60,592 70,280 75,740 135,791 140,560 151,480

Collatz Trajectory (78 steps to reach 1)

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

76,042,960 38,021,480 19,010,740 9,505,370 4,752,685 14,258,056 7,129,028 3,564,514 1,782,257 5,346,772 2,673,386 1,336,693 4,010,080 2,005,040 1,002,520 501,260 250,630 125,315 375,946 187,973 563,920 281,960 140,980 70,490 35,245 105,736 52,868 26,434 13,217 39,652 19,826 9,913 29,740 14,870 7,435 22,306 11,153 33,460 16,730 8,365 25,096 12,548 6,274 3,137 9,412 4,706 2,353 7,060 3,530 1,765 5,296 2,648 1,324 662 331 994 497 1,492 746 373

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