Question

Find the HCF of 125 and 240 using EDA.Also represent the HCF in the form of ax+by where x and y are given numbers and a,b are integers

Answer 1

HCF of 125 and 240

By using Euclid's division lemma to 125 and 240 we get

• 240=125×1+115

Since, Remainder 115≠0. we apply division lemma to Divisor 125 and Remainder 115 we get.

• 125=115×1+10

Since, Remainder 10≠0 . we apply division lemma to Divisor 115 and Remainder 10 we get.

• 115=10×11 +5

Since, Remainder 5≠0 . we apply division lemma to Divisor 10 and Remainder 5 we get.

• 10=5×2+0

Since Remainder =0

HCF of 125 and 240= 5

To represent the HCF as a linear combination of the given two numbers, we start from the last but one step and successively eliminate the previous reminder as follows:

• 5=115-10×11
• 5=115-(125-115×1)×11
• 5=115-125×11 +115×11
• 5=115×12 -125×11
• 5=(240-125×1)×12-125×11
• 5=240×12 -125×12 -125×11
• 5=240×12 -125×23

Therefore,

The HCF in the form of ax+by where x and y are given numbers and a,b are integers

• 5=240×12 -125×23