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Atlas › Integer Profiles › Node 8,009,540

8,009,540

22 × 5 × 72 × 11 × 743
Abundant Even Composite

8,009,540 factors as 2^2 × 5 × 7^2 × 11 × 743. Its 72 positive divisors give a proper-divisor sum of 13,364,092, so this integer is abundant. The Collatz stopping time is 116 steps.

Prime Factor Structure

Factorization String 2^2 × 5 × 7^2 × 11 × 743
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 21,373,632
Proper Divisor Sum 13,364,092
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #8009537 ← → #8009549

Radix Representation

Decimal 8009540
Binary 11110100011011101000100 (23 bits)
Octal 0o36433504
Hexadecimal 0x7A3744

Divisor Catalog (60 of 72)

1 2 4 5 7 10 11 14 20 22 28 35 44 49 55 70 77 98 110 140 154 196 220 245 308 385 490 539 743 770 980 1,078 1,486 1,540 2,156 2,695 2,972 3,715 5,201 5,390 7,430 8,173 10,402 10,780 14,860 16,346 20,804 26,005 32,692 36,407 40,865 52,010 57,211 72,814 81,730 104,020 114,422 145,628 163,460 182,035

Collatz Trajectory (116 steps to reach 1)

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

8,009,540 4,004,770 2,002,385 6,007,156 3,003,578 1,501,789 4,505,368 2,252,684 1,126,342 563,171 1,689,514 844,757 2,534,272 1,267,136 633,568 316,784 158,392 79,196 39,598 19,799 59,398 29,699 89,098 44,549 133,648 66,824 33,412 16,706 8,353 25,060 12,530 6,265 18,796 9,398 4,699 14,098 7,049 21,148 10,574 5,287 15,862 7,931 23,794 11,897 35,692 17,846 8,923 26,770 13,385 40,156 20,078 10,039 30,118 15,059 45,178 22,589 67,768 33,884 16,942 8,471

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