Question

If the HCF of 2048 and 960 is expressed in the form 960m-2048n find the value of m and n
​

Answer 1

The HCF of 2048 and 960 is 64.

So 960m-2048n= 64

960m = 64 - 2048n

30m = 2 - 64n ( simplified form) .......(1)

Now 64n = 2 - 30m ......... (2)

Put the value of 30m from eqn (1) in eqn (2)

So,

64n = 2 - (2-64)

64n = 2 - 2 - 64

64n = 64

(divide both sides by 64)

64n/64 = 64/64

n = 1

Now put the value of n= 1 in eqn 1

30m = 2 - 64 ( 1 )

30m = 2 - 64

30m = 62

(divide both sides by 30)

m = 62/ 30

m = 62/30

Now to prove the answer, put the values of n and m in the main equation.

2048n - 960m = 64

2048(1) - 960(62/ 30)= 64

2048 - 1984 = 64

I am getting the answers but I'm having some problems in the 64n = 2 - (2-64) step but the answers are correct.