Question

find the hcf of 75 and 243 using Euclid division algorithm express in the form 75m+243n and find m and n.

Plzz answer the question as quickly as possible....... ​

Answer 1

Given :  Two Numbers 75 & 243

To find : HCF using  Euclid division algorithm  and HCF to be expressed in form of 75m + 243n

Solution:

hcf of 75 and 243 using Euclid division algorithm e

243 = 75 * 3  + 18

75 = 18 * 4  + 3

18 = 3 * 6

3 is the HCF of 75 & 243

75 = 18 * 4  + 3

=> 3  = 75  - 18 * 4

18 = (243 - 3 * 75)

=> 3 = 75 - (243 - 3 * 75)  * 4

=> 3 = 75  - 4 * 243  + 12 * 75

=> 3 = 13 * 75  - 4 * 243

=> 3 = 75 * 13 - 243 * 4

Comparing with

3 = 75m + 243n

=> m = 13   &  n = - 4

3 is the HCF of 75 & 243

m = 13   &  n = - 4

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Answer 2

Answer:

First,

75=5*5*3= power of 5 is 2 *3

243=3*3*3*3*3 =power of 3 is 5

HCF =3(because it is the common digit in factors of 243 and 75.)

LCM=6075( because 5*5*3*3*3*3*3 is the greatest power of each prime factor ,involved in the number.)

Now,

HCF(a,b)*LCM(a,b)=a*b

3*6075=75*243

18225=18225

I hope it will help you...........

Step-by-step explanation: