To find the number of factors of a
number
If a number N can be expressed as product of prime factors
such that
N = pa x qb x rc...............................
Then, the total number of factors including N and 1 is given
by
(a + 1)x(b + 1)x(c + 1).................................
Example:
Find the total number of factors of 222.
222 = 2 x 3 x 37
Or, 222 = 21 x 31 x 371
So, the total number of factors = (1+1)x(1+1)x(1+1) = 2x2x2
= 8
We can check the answer as shown below.
The factors of 222 are 1, 2, 3, 6, 37, 74, 111, 222.
Find the total number of factors of 64.
64 = 26
So, the total number of factors = (6+1) = 7
We can check the answer as shown below.
The factors of 64 are 1, 2, 4, 8, 16, 32, 64.
Thanks for sharing the sample question on factors. Please share more details with question and answers. This is very useful in preparing for IMO Exams and the pattern of the Olympiad Exam.
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