How many factors does this number have
Number Theory
Level
2
How many positive divisors does the number 868 have. Include both 1 and 868 while calculating your answer.
The answer is 12.
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1 solution
Any number N can be written as a product of its prime factors for example N = P1^a * P2^b* P3^c where P1, P2 and P3 are prime numbers. The number of divisiors of N can be calculated as (a+1) (b+1) (c+1).
In this case 868 can be written as 2 x 2 x 7 x 31 or 868 in terms of its prime factors is 2^2 *7 *31 . Hence the number of divisors of 868 is 3 x 2 x 2 = 12.
We can also list out the divisors of 868 as 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, and 868