Question

If a = 2p x 3q x 5r and b = p2 x q3 x r5, where p, q, and r are primes , find the value of p + q + r , given that a =


b.

Answer 1

If a and b are any two composite numbers, they must have different prime factorizations. But since we have a = b given to us, then the prime factorizations must be the same.

Thus, $a = 2^p3^qr^5 = b = p^2q^3r^5$

Hence, $p = 2, q = 3, r = 5$

$p + q + r = 2 + 3 + 5 = 10$

Ans: 10