If B = 12 x 15 x 34, then all of the following answer choices are inte

Solution

• \(B = 12*15*34 = (2^2*3)*(3*5)*(2*17) = 2^3*3^2*5*17\)
• So, If B is divided by any integer whose prime factorization either contains prime numbers other than 2, 3, 5, and 17 or it has powers of at least one of 2, 3, 5, and 17 more than that in B, then the result will be non-integer.
• So, let’s check the answer options:

o Option A : B/18

 \(18 = 2*3^2\)
 Since powers of 2 and 3 are less than or equal to that in B, so B/18 it will be an integer.
o Option B: B/30

 30 = 2*3*5
 Since powers of 2, 3 and 5 are less than or equal to that in B, So, B/30 will be an integer.
o Option C: B/32

 \(32 = 2^5\)
 Since powers of 2 is more than that of the power of 2 in B. Hence, B/32 will not be an integer.