Question

Express the HCF of 152 and 272 as 152 x + 272 y, where x and y are integers.

Answer 1

Answer:

On applying the Euclid’s division lemma to find HCF of 152, 272, we get

272=152×1+120

Here the remainder = 0.

Using Euclid’s division lemma to find the HCF of 152 and 120, we get

152=120×1+32

Again the remainder = 0.

Using division lemma to find the HCF of 120 and 32, we get

120=32×3+24

Similarly,

32=24×1+8

24=8×3+0

HCF of 272 and 152 is 8.

272×8 + 152x = H.C.F. of the numbers

⇒ 8=272×8+152x  

⇒  8−272×8=152x

⇒8(1−272)=152x

⇒x=−2168152=−27119

Step-by-step explanation: