Question

If N=2 cubed cross times 3 to the power of 4 space, M=2 squared cross times 3 cross times 5, then find the number of factors of N that are common with the factors of M

Answer 1

Given : N =   2³  ×  3⁴  , M =   2²  × 3 × 5

To find :  number of factors of N that are common with the factors of M

Solution:

N =   2³  ×  3⁴

M =   2²  × 3 × 5

N =   2³  ×  3⁴  

=> N = 2 × 2² × 3  ×  3³

M =   2²  × 3 × 5

2²  × 3  is common  in N & M

number of common factors = (2 + 1)(1 + 1)

= 3 * 2 = 6

1 , 2  ,  3  , 4 , 6  , 12

number of factors of N that are common with the factors of M  are 6

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