If 78 and 66 are both factors of x, what is the smallest number of fac

Question

If 78 and 66 are both factors of the positive integer x, what is the smallest number of positive factors x could have in total?

A. 12
B. 16
C. 18
D. 24
E. 36

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nick1816 · Answer

LCM(66,78)= 2*3*11*13

Hence, x= 2*3*11*13*k, where k is a positive integer.

x will have smallest number of factors, if k is equal to 1.

smallest number of positive factors x could have in total= 2*2*2*2=16

exc4libur · Answer

f(x)= = ; gcf = 
min.f(x)=min.f(2*3*13*11)=(1+1)(1+1)(1+1)(1+1)=16

Ans (B)

TheNightKing · Answer

78 = 2*3*13

66 = 2*3*11

Since both are factors of x then x will have 2*3*11*13.

Now we need to calculate positive factors of x so look at it this way. We can either pick a number or drop a number. So we have 2 options for each of these. So we have 2*2*2*2 factors possible and that's 16.

Abhishek009 · Answer

LCM ( 78, 66) = 858

Now,  858 = 2^1 3^1 11^1 13^1

So, No of factors of 858 = (1+1)(1+1)(1+1)(1+1) => 16 , Answer must be (B)

hiranmay · Answer

If 78 and 66 are both factors of the positive integer x, what is the smallest number of positive factors x could have in total?

A. 12
B. 16 -->   correct : the smallest number x that is divisible by 78 & 66 i.e the smallest number x = LCM (78, 66) = LCM (2*3*13, 2*3*11) =  2^1*3^1*11^1*13^1 ; so number of positive factors x = (1+1)*(1+1)*(1+1)*(1+1) = 2^4 = 16 
C. 18
D. 24
E. 36

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If 78 and 66 are both factors of x, what is the smallest number of fac

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If 78 and 66 are both factors of x, what is the smallest number of fac

Prep Toolkit

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