The number of possible pairs of numbers, whose product is 5400 and HCF

1.	The number of possible pairs of numbers, whose product is 5400 and HCF is 30, is1. 12. 23. 34. None of the above
Answer» Correct Answer - Option 2 : 2 Given: Product of numbers = 5400 HCF of numbers = 30 Formula required: Product of two numbers = LCM of two number × HCF of two numbers Calculations: Let the numbers be '30a' '30b' 5400 = 30a × 30b ⇒ a × b = 5400/(30 × 30) ⇒ a × b = 6 Factors of 6 = 1, 2, 3, 6 Hence, we can write in 6 the form of a × b = (2 × 3) or (1 × 6) Hence, the pair of numbers is = [(30 × 2), (30 × 3)] or [(30 × 1), (30 × 6)] ⇒ (60, 90) or (30, 180) ∴ The possible number of pairs is 2

The number of possible pairs of numbers, whose product is 5400 and HCF is 30, is1. 12. 23. 34. None of the above

Answer» Correct Answer - Option 2 : 2

Given:

Product of numbers = 5400

HCF of numbers = 30

Formula required:

Product of two numbers = LCM of two number × HCF of two numbers

Calculations:

Let the numbers be '30a' '30b'

5400 = 30a × 30b

⇒ a × b = 5400/(30 × 30)

⇒ a × b = 6

Factors of 6 = 1, 2, 3, 6

Hence, we can write in 6 the form of a × b = (2 × 3) or (1 × 6)

Hence, the pair of numbers is = [(30 × 2), (30 × 3)] or [(30 × 1), (30 × 6)]

⇒ (60, 90) or (30, 180)

∴ The possible number of pairs is 2

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The number of possible pairs of numbers, whose product is 5400 and HCF is 30, is1. 12. 23. 34. None of the above

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