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Get access to the detailed solutions to the previous years questions asked in IIM IPMAT exam
Number of positive Integers dividing a given number = Number of factors of that number
Prime Factorization of
1890 = 2 × 33 × 5 × 7
Prime factorization of
130 = 2 × 5 × 13
Prime factorization of
170 = 2 × 5 × 17
Prime factorization of
1890 × 130 × 170 = (2 × 33 × 5 × 7) × (2 × 5 × 13) × (2 × 5 × 17)
= 23 × 33 × 53 × 7 × 13 × 17
Number of factors of
1890 × 130 × 170 = (3 + 1) (3 + 1) (3 + 1) (1 + 1) (1 + 1) (1 + 1)
= 4 × 4 × 4 × 2 × 2 × 2
Number of factors multiple of 45
= 32 × 5 × (23 × 3 × 52 × 7 × 13 × 17)
= 45 (23 × 3 × 52 × 7 × 13 × 17)
= (3 + 1) (1 + 1) (2 + 1) (1 + 1) (1 + 1) (1 + 1)
= 4 × 2 × 3 × 2 × 2 × 2
= 192 factors
Number of positive integers that divide 1890 × 130 × 170 are not divisible by 45 is = Total factors − number of factors multiple of 45
= 512 – 192
= 320 factors