λ
Ratio Atlas
Atlas › Integer Profiles › Node 8,091,824

8,091,824

24 × 13 × 38903
Abundant Even Composite

8,091,824 factors as 2^4 × 13 × 38903. Its 20 positive divisors give a proper-divisor sum of 8,792,512, so this integer is abundant. The Collatz stopping time is 137 steps.

Prime Factor Structure

Factorization String 2^4 × 13 × 38903
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 20
Divisor Sum (σ) 16,884,336
Proper Divisor Sum 8,792,512
Digit Sum / Digital Root 32 (Root: 5)
Adjacent Primes #8091821 ← → #8091829

Radix Representation

Decimal 8091824
Binary 11110110111100010110000 (23 bits)
Octal 0o36674260
Hexadecimal 0x7B78B0

Divisor Catalog (20)

1 2 4 8 13 16 26 52 104 208 38,903 77,806 155,612 311,224 505,739 622,448 1,011,478 2,022,956 4,045,912 8,091,824

Collatz Trajectory (137 steps to reach 1)

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

8,091,824 4,045,912 2,022,956 1,011,478 505,739 1,517,218 758,609 2,275,828 1,137,914 568,957 1,706,872 853,436 426,718 213,359 640,078 320,039 960,118 480,059 1,440,178 720,089 2,160,268 1,080,134 540,067 1,620,202 810,101 2,430,304 1,215,152 607,576 303,788 151,894 75,947 227,842 113,921 341,764 170,882 85,441 256,324 128,162 64,081 192,244 96,122 48,061 144,184 72,092 36,046 18,023 54,070 27,035 81,106 40,553 121,660 60,830 30,415 91,246 45,623 136,870 68,435 205,306 102,653 307,960

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