Find the HCF of 65 and 117 and express it in the form of 65m + 117n
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Answered by
4
Hello there !
Euclid's Division Lemma :-
a = bq +r
117 > 65
117 = 65 × 1 + 52 ----> [ 2 ]
65 = 52 x 1 + 13 -----> [1]
52 = 13 x 4 + 0
HCF = 13
13 = 65m + 117n
From [ 1] ,
13 = 65 - 52 x 1
From [2] ,
52 = 117 - 65 x 1 ----> [3]
Hence ,
13 = 65 - [ 117 - 65 x 1 ] ------> from [3]
= 65 x 2 - 117
= 65 x 2 + 117 x [-1 ]
m = 2
n = -1
Hope this Helped You !
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Euclid's Division Lemma :-
a = bq +r
117 > 65
117 = 65 × 1 + 52 ----> [ 2 ]
65 = 52 x 1 + 13 -----> [1]
52 = 13 x 4 + 0
HCF = 13
13 = 65m + 117n
From [ 1] ,
13 = 65 - 52 x 1
From [2] ,
52 = 117 - 65 x 1 ----> [3]
Hence ,
13 = 65 - [ 117 - 65 x 1 ] ------> from [3]
= 65 x 2 - 117
= 65 x 2 + 117 x [-1 ]
m = 2
n = -1
Hope this Helped You !
mark as brainliest
Answered by
6
let the two positive integers as a and b
a=117
b=65
a<b
a/b
Euclid's Division algorithm as follows :
117=65×1+52(1)
65=52×1+13(2)
52=13×4+0(3)
therefore HCF=13
to express it in the linear combination of the given two numbers,we start from last one step and successively eliminate the previous remainders as follows:
from (2),we have
13=65-52×1
13=65-(117-65×1)
13=65-117+65×1
13=65×2+117×(-1)
13=65-117+65×1
13=65m+117n[where m=2,n=-1]
hope it helps
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