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Atlas › Integer Profiles › Node 8,107,785

8,107,785

32 × 5 × 72 × 3677
Abundant Odd Composite

8,107,785 factors as 3^2 × 5 × 7^2 × 3677. Its 36 positive divisors give a proper-divisor sum of 8,244,603, so this integer is abundant. The Collatz stopping time is 199 steps.

Prime Factor Structure

Factorization String 3^2 × 5 × 7^2 × 3677
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 16,352,388
Proper Divisor Sum 8,244,603
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #8107769 ← → #8107787

Radix Representation

Decimal 8107785
Binary 11110111011011100001001 (23 bits)
Octal 0o36733411
Hexadecimal 0x7BB709

Divisor Catalog (36)

1 3 5 7 9 15 21 35 45 49 63 105 147 245 315 441 735 2,205 3,677 11,031 18,385 25,739 33,093 55,155 77,217 128,695 165,465 180,173 231,651 386,085 540,519 900,865 1,158,255 1,621,557 2,702,595 8,107,785

Collatz Trajectory (199 steps to reach 1)

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

8,107,785 24,323,356 12,161,678 6,080,839 18,242,518 9,121,259 27,363,778 13,681,889 41,045,668 20,522,834 10,261,417 30,784,252 15,392,126 7,696,063 23,088,190 11,544,095 34,632,286 17,316,143 51,948,430 25,974,215 77,922,646 38,961,323 116,883,970 58,441,985 175,325,956 87,662,978 43,831,489 131,494,468 65,747,234 32,873,617 98,620,852 49,310,426 24,655,213 73,965,640 36,982,820 18,491,410 9,245,705 27,737,116 13,868,558 6,934,279 20,802,838 10,401,419 31,204,258 15,602,129 46,806,388 23,403,194 11,701,597 35,104,792 17,552,396 8,776,198 4,388,099 13,164,298 6,582,149 19,746,448 9,873,224 4,936,612 2,468,306 1,234,153 3,702,460 1,851,230

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