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H.C.F and L.C.M of two numbers are 4 and 308 respectively. Find the sum of the digits of the number, lies between “30 – 50”.1. 22. 83. 64. 7 |
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Answer» Correct Answer - Option 2 : 8 Given: H.C.F of two numbers = 4 L.C.M of two numbers = 308 One of the numbers lies between “30 – 50” Concept used: If H.C.F of two natural numbers is H, then numbers should be Hx and Hy respectively. Where x and y should be relatively prime number. Formula used: The Product of H.C.F and L.C.M of any two numbers is equal to the product of that numbers. Calculation: H.C.F of two numbers = 4 Let, numbers = 4x and 4y respectively Using formula, 4x × 4y = 4 × 308 (Given) ⇒ x × y = 308/4 = 77 ⇒ x × y = 77 Possibilities of x and y are (1, 7) and (77, 11) [Both sets are co – prime] Taking x = 1 and y = 77 Numbers are 1 × 4 = 4 and 77 × 4 = 308 None of the numbers lie between 30 -50, therefore we can’t take these numbers. Now, taking x = 7 and y = 11 Numbers are 7 × 4 = 28 and 11 × 4 = 44 And 44 lies between “30- 50” ∴ Sum of the digits = 4 + 4 = 8 |
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