The HCF of two numbers is 16 and their LCM is 160. If one of the numbers is…

For any two positive integers, the product of the two numbers is always equal to the product of their HCF and their LCM.

1. Let the two numbers be 32 and n, where the HCF is 16 and the LCM is 160.

2. Using the identity, 32 multiplied by n equals HCF multiplied by LCM, so 32 multiplied by n equals 16 multiplied by 160, which is 2560.

3. Solving for n gives n equals 2560 divided by 32, which is 80.

Checking 32 and 80 by prime factorisation: 32 = 25 and 80 = 24 × 5. The HCF, formed from the lowest powers of the common prime factors, is 24 = 16, and the LCM, formed from the highest powers of all prime factors involved, is 25 × 5 = 160, both matching the values given in the question, confirming that the other number is 80.