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Divisor Count Conclusion (Posted on 2015-03-06) Difficulty: 3 of 5
Determine the total number of positive divisors of 1890*1930*1970 such that none of the said divisors is divisible by 45.

No Solution Yet Submitted by K Sengupta    
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solution | Comment 1 of 2
first the prime factorizations 1890*1930*1970=2^3*3^3*5^3*7*193*197
45=3^2*5

The number of factors of the big number containing no 3's or 5's is 4*2*2*2=32

The number of factors of 3^3*5^3 not multiples of 45 is 10:
5^{0,1,2,3}, 3*5^{0,1,2,3}, 3^2, 3^3

32*10=320

  Posted by Jer on 2015-03-06 08:46:17
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