Question

Express the HCF of 234 and 111 as 234x and 111 y where x and y are integer find the value of x and y

Answer 1

The value of x and y for expressing the H C F of numbers is - 9 , 19  

Step-by-step explanation:

Given as :

The two numbers are 234 , 111

The H C F of number 234 and 111  express as 234 x and 111 x

According to question

H C F of number 234 can be find as

234 = 2 x 3 x 3 x 13

And, H C F of number 111 can be find as

111 = 3 × 37

∴ From both numbers , The H C F = 3

Now, expressing the H C F of both number in x , y terms

we can write it  3 as

3 = 111 - (12 × 9)

3 = 111 -  (234 - 111 × 2) × 9                            [we can write 12 = 234 - 111 × 2]

3 = 111 - ( 234 × 9 - 111 × 2 × 9 )

3 = 111 - ( 234 × 9 ) + ( 111 × 18 )

3 = 111 + ( 111 × 18 )  - ( 234 × 9 )

3 = 111 ( 1 + 18 ) - 234 × 9

3 = 111 × 19 - 234 × 9

3 = 234 × (-9) + 111 × 19

So, The H C F of numbers 234 and 111 in the form of 234 x and 111 y =  234 × (-9) + 111 × 19  

So, The value of x = - 9

And The value of y = 19

Hence, The value of x and y for expressing the H C F of numbers is - 9 , 19  Answer