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17 Nov 2025, 22:31
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If x = 6p, where p is a positive integer greater than 7, what is the minimum possible number of factors of x?
A. 7
B. 8
C. 9
D. 10
E. Greater than 10
A. 7
B. 8
C. 9
D. 10
E. Greater than 10
18 Nov 2025, 01:41
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x = 6p , or 2*3
Number of factors of a number x = a^n * b^m = (n+1) * (m+1)
To minimize
Two cases come to mind logically.
The first is that p is a prime, as that is associated with low number of factors.
Take 11, for example, then factors = 11 * 2 * 3 -> Number of factors: (1+1)*(1+1)*(1+1) = 8
The other is that p is a combination of the factors of 6 that is higher than 7, like for example 9 or 12 ->
Take 9 -> Number of factors 4 * 2 = 8 ; Take 12 -> Number of factors: 4* 3 = 12
ANS: B.
Number of factors of a number x = a^n * b^m = (n+1) * (m+1)
To minimize
Two cases come to mind logically.
The first is that p is a prime, as that is associated with low number of factors.
Take 11, for example, then factors = 11 * 2 * 3 -> Number of factors: (1+1)*(1+1)*(1+1) = 8
The other is that p is a combination of the factors of 6 that is higher than 7, like for example 9 or 12 ->
Take 9 -> Number of factors 4 * 2 = 8 ; Take 12 -> Number of factors: 4* 3 = 12
ANS: B.
18 Nov 2025, 21:23
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If p is greater than 7 than we can have p = 8 6(8) 48, which has the factors 1, 2, 3, 4, 5, 6, 8, 12, 16, 24, 48. So the least number of factors would be 10
