Question

find the HCF of 52 and 117 and express it in form 52x + 117y ?​

Answer 1

Step-by-step explanation:

Between 65 and 117; 117 is greater than 65 Division lemma of 117 and 65: ⇒ 117 = 65 x 1 + 52 ⇒ 65 = 52 x 1 + 13 ⇒ 52 = 4 x 13 + 0 In this step the remainder is zero. Thus, the divisor i.e. 13 in this step is the H.C.F. of the given numbers The H.C.F. of 65 and 117 is 13 Now, 13 = 65 – 52 x 1 ⇒ 52 = 117 – 65 x 1 ⇒ 13 = 65 – (117 – 65 x 1) x 1 ⇒ 13 = 65 x 2 – 117 ⇒ 13 = 65 x 2 + 117 x (–1) Therefore H.C.F. of 65 and 117 is of the form 65m + 117n, where m = 2 and n = –1.