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03 Feb 2026, 00:04
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
66% (02:07) correct
34%
(02:30)
wrong
based on 146
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The positive integer P is divisible by 42. The product P x Q is divisible by 180. Which of the following must be a factor of P x Q?
A. 16
B. 27
C. 49
D. 144
E. 630
A. 16
B. 27
C. 49
D. 144
E. 630
03 Feb 2026, 06:28
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p is divisible by 42. so p is multiple of 42.
prime factorization of 42 =2* 3 * 7
p * q is divisible by 180
180 = 2^2 * 3^2 * 5
now we know p is divisible by 42 and p*q is divisible by 180
so we can take the LCM of this both.
so we can say that p*q have minimun of 2^2 * 3^2 * 5 * 7
so we need to see which option can have this factors in its prime factorization
only option E can satisfy such requirements.
prime factorization of 42 =2* 3 * 7
p * q is divisible by 180
180 = 2^2 * 3^2 * 5
now we know p is divisible by 42 and p*q is divisible by 180
so we can take the LCM of this both.
so we can say that p*q have minimun of 2^2 * 3^2 * 5 * 7
so we need to see which option can have this factors in its prime factorization
only option E can satisfy such requirements.
ExpertsGlobal5
03 Feb 2026, 08:57
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Given: P is divisible by 42
42 = 2*3*7
It is also given that: P*Q is divisible by 180
180 = (2^2)*(3^2)*5
Hence, P*Q must contain (2^2)*(3^2)*5*7
Now, let's check all the options, one by one:
Option A - 16 => 2^4 => Not guaranteed
Option B - 27 => 3^3 => Not guaranteed
Option C - 49 => 7^2 => Not guaranteed
Option D - 144 => (2^4)*(3^2) => Extra 2's present
Option E - 630 => 2*(3^2)*5*7 => All guaranteed
Hence, the correct answer is Option E - 630.
Hope this helps!
42 = 2*3*7
It is also given that: P*Q is divisible by 180
180 = (2^2)*(3^2)*5
Hence, P*Q must contain (2^2)*(3^2)*5*7
Now, let's check all the options, one by one:
Option A - 16 => 2^4 => Not guaranteed
Option B - 27 => 3^3 => Not guaranteed
Option C - 49 => 7^2 => Not guaranteed
Option D - 144 => (2^4)*(3^2) => Extra 2's present
Option E - 630 => 2*(3^2)*5*7 => All guaranteed
Hence, the correct answer is Option E - 630.
Hope this helps!
