Choose the correct answer.Written as the product of its prime factors 308 = 22 × 7 × 11 and 952 = 23 × 7 × 17. Find the smallest integer value of q such that 308q is a multiple of 952.11344513

To find the smallest integer value of q such that 308q is a multiple of 952, we need to compare the prime factorization of both numbers.

The prime factorization of 308 is 2^2 × 7 × 11 and the prime factorization of 952 is 2^3 × 7 × 17.

For 308q to be a multiple of 952, it must contain all the prime factors of 952 to at least the same power.

Comparing the prime factors:

• Both have a factor of 2, but 952 has 2 to the power of 3 while 308 only has 2 to the power of 2. So, we need at least one more factor of 2.

• Both have a factor of 7, so we don't need any more of those.

• 308 has a factor of 11, but 952 doesn't, so the factor of 11 doesn't affect our answer.

• 952 has a factor of 17, but 308 doesn't. So, we need a factor of 17.

The smallest number that has a factor of 2 and a factor of 17 is 2 × 17 = 34.

So, the smallest integer value of q such that 308q is a multiple of 952 is 34.