Question

13. If the HCF of 408 and 1032 is expressible in the form of 1032m
- 408x5, find m​

Answer 1

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\times51032m−408×5

To find : The value of m?

Solution :

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

1032 = 408\times2 + 2161032=408×2+216

408 = 216\times1 + 192408=216×1+192

216 = 192\times1 +24216=192×1+24

192 = 24\times8 + 0192=24×8+0

Now, The rest becomes 0.

So, HCF of 408 and 1032 is 24

According to question,

HCF=1032m-408\times5HCF=1032m−408×5

24=1032m-408\times524=1032m−408×5

24=1032m-204024=1032m−2040

24+2040=1032m24+2040=1032m

1032m=20641032m=2064

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

1032

2064

m=2m=2

Therefore, The value of m is 2.