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The Highest Common Factor of two numbers is (2/5)th of their Least Common Multiple. If the product of two numbers is 1690, then what is their Highest Common Factor?

The Highest Common Factor of two numbers is (2/5)th of their Least Common Multiple. If the product of two numbers is 1690, then what is their Highest Common Factor? Correct Answer 26

Given:

HCF of two numbers = (2/5) × (LCM of two numbers)

The product of two numbers = 1690

Concept:

LCM × HCF = Product of two number

Calculation:

⇒ HCF = (2/5) × LCM

⇒ LCM = (5/2) × HCF

⇒ The product of two number = HCF × LCM

⇒ 1690 = HCF × LCM

⇒ 1690 = (HCF) × (5/2) × (HCF)

⇒ (HCF)2 = (1690 × 2)/5 = 338 × 2 = 676

⇒ HCF = √676 = 26

∴ The required result will be 26. 

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