Question
Calculate the number of factors of 480.
Solution
If prime factorization of a number 'N' = a p  X b q  X c r , then number of factors of 'N' are product of (p + 1) , (q + 1) and (r + 1) together.
480 = 2 x 2 x 2 x 2 x 2 x 3 x 5 = 2 5 Â x 3 1 Â x 5 1
So, total number of factors = (5 + 1) x (1 + 1) x (1 + 1) = 6 x 2 x 2 = 24
The least number which when divided by 6, 7, 10, 13, and 15 leaves the same remainder 5 in each case, is:
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