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Find the number of divisors of 3780 that are multiples of 3.

 Sep 7, 2020
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Note that 3780=2^2*3^3*5*7. In order for a divisor to be a multiple of 3, we need at least one 3 in the divisors prime factorization. We can have 2^0,2^1, or 2^2. We can have 3^1,3^2,3^3 (not 3^0). We can have 5^0,5^1. We can have 7^0,7^1. So it is 3*3*2*2=9*4=36

 

Another solution. We can count all the ways that we can't get a 3. That is when we have 3^0, so 2^0,2^1,2^2 and 5^0,5^1 and 7^0,7^1. Total divisors is 3*4*2*2=48. We subtract 3*2*2=12. So 48-12=36 again.

 

Hope this helped!

 Sep 7, 2020

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