Question

The product of 2 two digit numbers is 300 and their HCF is 5. What are the numbers?

Answer 1

Given that HCF of 2 numbers is 5

The numbers may like 5x and 5y

Also given their product = 300

5x × 5y = 300

⇒ 25xy = 300

⇒ xy = `300/25`

⇒ xy = 12

The possible values of x and y be (1, 12) (2, 6) (3, 4)

The numbers will be (5x, 5y)

⇒ (5 × 1, 5 × 12) = (5, 60)

⇒ (5 × 2, 5 × 6) = (10, 30)

⇒ (5 × 3, 5 × 4) = (15, 20)

(5, 60) is impossible because the given the numbers are two digit numbers.

The remaining numbers are (10, 30) and (15, 20)

But given that HCF is 5

(10, 30) is impossible, because its HCF = 10

The numbers are 15, 20