Question

Find the hcf of number 72 and 96 by euclid's division algorithm and express it in the form 96 m + 72 and where m and n are integers

Answer 1

Applying Euclid's Division algorithm

to 72 and 96 , we get

96 = 72 × 1 + 24 ----( 1 )

72 = 24 × 3 + 0 -----( 2 )

Therefore 24 is the HCF of 72 and 96

From ( 1 ),

24 = 96 - 72 × 1

= 96 ( 1 ) + 72 × ( - 1 )

It is in the form of

= 96m + 72n