Question

Use the Euclid's division algorithm to find the HCF of 180, 252 and 324. 2 marks question

Answer 1

Answer:

HCF of 180, 252 and 324:

324 = 1 x 180 + 144

180 = 1 x 144 + 36

144 = 4 x 36 + 0

So, HCF of 324 and 180 = 36

HCF of 252 and 36:

252 = 7 x 36 + 0

So, HCF of 252 and 36 is 36.

Hence, the HCF of 180, 252 and 324 is 36.

Answer 2

Step-by-step explanation:

Given:-

180, 252 and 324

To find:-

Use the Euclid's division algorithm to find the HCF of 180, 252 and 324.

Solution:-

Given numbers are 180, 252 and 324

Euclid's Division Lemma:-

For any two integers a and b there exist two integers q and r satisfying a =bq+r , 0≤r<b .

We have to find the HCF first any two numbers

HCF of 180 and 252:-

Let a = 252 and b = 180

On writting a= bq+r

252=180×1 +72

Consider a = 180 and b = 72

On writting a= bq+r

180=72×2+36

Consider a = 72 and b=36

On writting a= bq+r

72 = 36×2+0

HCF(252,180) = 36

HCF of 324 and 36:-

Let a = 324 and b= 36

On writting a= bq+r

=> 324 = 36×9+0

HCF(324,36) = 36

HCF(180,252,324) = 36

Answer:-

HCF of 180,252,324 is 36

Used formula:-

Euclid's Division Lemma:-

For any two integers a and b there exist two integers q and r satisfying a =bq+r , 0≤r<b .