Question

if the HCF of 408 and 1032 is expressible in the form 1032m-408×5,find m

Answer 1

By Euclid 's division algorithm,

1032 = 408×2 + 216

408 = 216×1 + 192

216 = 192×1 + 24

192 = 24×8 + 0

Therefore rem=0, 

so HCF  is 24

1032m - 408*5 = HCF of these numbers

1032m- 2040 = 24

1032m = 24+2040

m = 2064/1032=2

Therefore, m=2.

Answer 2

Answer:

The value of m is 2.

Step-by-step explanation:

Given : If the HCF of 408 and 1032 is expressible in the form $1032m-408\times5$

To find  : The value of m?

Solution :

If the HCF of 408 and 1032 will be written using division rule,

$1032 = 408\times2 + 216$

$408 = 216\times1 + 192$

$216 = 192\times1 +24$

$192 = 24\times8 + 0$

Now, The rest becomes 0.

So, HCF of 408 and 1032 is 24

According to question,

$HCF=1032m-408\times5$

$24=1032m-408\times5$

$24=1032m-2040$

$24+2040=1032m$

$1032m=2064$

$m=\frac{2064}{1032}$

$m=2$

Therefore, The value of m is 2.