Express the hcf of number 72 and 124 as a linear combination

1.	Express the hcf of number 72 and 124 as a linear combination
Answer» Consider the following numbers72 and 124First find the HCF of above numbers.72 = 2\xa0× 2\xa0× 2\xa0× 3\xa0× 3\xa0⇒ 2³\xa0× 3²124 = 2\xa0× 2\xa0× 31⇒ 2²\xa0× 31To find the HCF of these numbers, take the least power of each common factor and find the product.Here 2 is the only common factor and least power of which is 2.So, we haveHCF(72 and 124) = 4Now we need to express HCF = 4 as a linear combination of 72 and 124.That is,4 = 72a + 124b, where a and b are integers.Use hit and trial method.Take a = -10 and b = 672(-10) + 124(6)\xa0⇒ -720 + 744 = 24, which is not equal to 4.So, take a = -12 and b =772(-12) + 124(7)⇒ - 864 + 868 = 4So, the required linear combination isHCF(72 and 124) = 4 = 72(-12) + 124(7)

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