Find the HCF of the pair of integers and express it as a linear combin

1.	Find the HCF of the pair of integers and express it as a linear combination of them 1288 and 575.
Answer» By applying Euclid’s division lemma on 1288 and 575, we get 1288 = 575 x 2+ 138………… (1) As the remainder ≠ 0, apply division lemma on divisor 506 and remainder 143 575 = 138 x 4 + 23……………. (2) As the remainder ≠ 0, apply division lemma on divisor 143 and remainder 77 138 = 23 x 6 + 0……………….. (3) Thus, we can conclude the H.C.F. = 23. Now, in order to express the found HCF as a linear combination of 1288 and 575, we perform 23 = 575 – 138 x 4 [from (2)] = 575 – [1288 – 575 x 2] x 4 [from (1)] = 575 – 1288 x 4 + 575 x 8 = 575 x 9 – 1288 x 4

Find the HCF of the pair of integers and express it as a linear combination of them 1288 and 575.

Answer»

By applying Euclid’s division lemma on 1288 and 575, we get

1288 = 575 x 2+ 138………… (1)

As the remainder ≠ 0, apply division lemma on divisor 506 and remainder 143

575 = 138 x 4 + 23……………. (2)

As the remainder ≠ 0, apply division lemma on divisor 143 and remainder 77

138 = 23 x 6 + 0……………….. (3)

Thus, we can conclude the H.C.F. = 23.

Now, in order to express the found HCF as a linear combination of 1288 and 575, we perform

23 = 575 – 138 x 4 [from (2)]

= 575 – [1288 – 575 x 2] x 4 [from (1)]

= 575 – 1288 x 4 + 575 x 8

= 575 x 9 – 1288 x 4