The HCF and LCM of two numbers are 33 and 264 respectively. When the first number is completely divided by 2, the quotient is 33. Find the other number.

We can use the formula that explains the relationship between the LCM and HCF of two numbers and solve this problem.

Answer: If the HCF and LCM of two numbers are 33 and 264 respectively, and when the first number is completely divided by 2 for which the quotient is 33, the other number is 132.

Let's solve this step by step.

Explanation:

Let the first number be a and the other number is b.

Therefore, LCM (a,b) = 264 and HCF (a,b) = 33

Since, the first number is completely divided by 2, the quotient is 33, a = 2 × 33 = 66

As we know a × b = LCM(a,b) × HCF(a,b)

Then b = [LCM(a,b) × HCF(a,b)] ÷ a

b = (264 × 33) ÷ 66 = 132

Thus, if the HCF and LCM of two numbers are 33 and 264 respectively, and when the first number is completely divided by 2 for which the quotient is 33, the other number is 132.