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If a three digit number ‘xyz’ has 3 factors, how many factors does the

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If a three digit number ‘xyz’ has 3 factors, how many factors does the  [#permalink]

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New post 20 Oct 2017, 08:44
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If a three digit number ‘xyz’ has 3 factors, how many factors does the 6-digit number ‘xyzxyz’ have?

A. 16 factors
B. 20 factors
C. 24 factors
D. 16 or 20 factors
E. 16 or 24 factors

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If a three digit number ‘xyz’ has 3 factors, how many factors does the  [#permalink]

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New post 20 Oct 2017, 08:56
Mahmud6 wrote:
If a three digit number ‘xyz’ has 3 factors, how many factors does the 6-digit number ‘xyzxyz’ have?

A. 16 factors
B. 20 factors
C. 24 factors
D. 16 or 20 factors
E. 16 or 24 factors


\(xyzxyz=xyz*1001=xyz*7*11*13\)
and \(xyz = a^2\) as it has ONLY 3 factors so it is SQUARE of prime number..
so \(xyzxyz=a^2*7*11*13\)..
two possibilities now:-
1) if a is a different PRIME, number of factors = 3*2*2*2=24..
2) If a is one of 7,11 or 13 # = 11^3*7*13 = 4*2*2=16

so 16 or 24

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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If a three digit number ‘xyz’ has 3 factors, how many factors does the &nbs [#permalink] 20 Oct 2017, 08:56
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