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

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Retired Moderator
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 497
If a three digit number ‘xyz’ has 3 factors, how many factors does the  [#permalink]

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20 Oct 2017, 07:44
1
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Difficulty:

55% (hard)

Question Stats:

50% (01:39) correct 50% (02:16) wrong based on 36 sessions

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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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Hasan Mahmud

Math Expert
Joined: 02 Aug 2009
Posts: 7198
If a three digit number ‘xyz’ has 3 factors, how many factors does the  [#permalink]

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20 Oct 2017, 07:56
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

E
_________________

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, 07:56
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# If a three digit number ‘xyz’ has 3 factors, how many factors does the

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