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Atlas › Integer Profiles › Node 8,577,140

8,577,140

22 × 5 × 11 × 13 × 2999
Abundant Even Composite

8,577,140 factors as 2^2 × 5 × 11 × 13 × 2999. Its 48 positive divisors give a proper-divisor sum of 12,590,860, so this integer is abundant. The Collatz stopping time is 150 steps.

Prime Factor Structure

Factorization String 2^2 × 5 × 11 × 13 × 2999
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 21,168,000
Proper Divisor Sum 12,590,860
Digit Sum / Digital Root 32 (Root: 5)
Adjacent Primes #8577133 ← → #8577161

Radix Representation

Decimal 8577140
Binary 100000101110000001110100 (24 bits)
Octal 0o40560164
Hexadecimal 0x82E074

Divisor Catalog (48)

1 2 4 5 10 11 13 20 22 26 44 52 55 65 110 130 143 220 260 286 572 715 1,430 2,860 2,999 5,998 11,996 14,995 29,990 32,989 38,987 59,980 65,978 77,974 131,956 155,948 164,945 194,935 329,890 389,870 428,857 659,780 779,740 857,714 1,715,428 2,144,285 4,288,570 8,577,140

Collatz Trajectory (150 steps to reach 1)

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

8,577,140 4,288,570 2,144,285 6,432,856 3,216,428 1,608,214 804,107 2,412,322 1,206,161 3,618,484 1,809,242 904,621 2,713,864 1,356,932 678,466 339,233 1,017,700 508,850 254,425 763,276 381,638 190,819 572,458 286,229 858,688 429,344 214,672 107,336 53,668 26,834 13,417 40,252 20,126 10,063 30,190 15,095 45,286 22,643 67,930 33,965 101,896 50,948 25,474 12,737 38,212 19,106 9,553 28,660 14,330 7,165 21,496 10,748 5,374 2,687 8,062 4,031 12,094 6,047 18,142 9,071

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