Question

Use Euclid's Division Algorithm to find HCF of :→
1260 , 7344​

Answer 1

7344=1260×5+1044

1260=1044×1 +216

1044=216×4+180

216=180×1+36

180=36×5+0

h.cf=36

Answer 2

Step-by-step explanation:

Given :-

1260 and 7344

To find :-

Find HCF of the numbers by using Euclid's Division Lemma?

Solution:-

Given numbers are 1260 and 7344

We know that

Euclids Division Lemma:-

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

Let a = 7344 and b = 1260

On writing a = bq+r

=> 7344 = 1260 ×5 + 1044

Let a = 1260 and b = 1044

On writing a = bq+r

=> 1260 = 1044×1+216

Let a = 1044 and b = 216

On writing a = bq+r

=> 1044 = 216×4 + 180

Let a = 216 and b = 180

On writing a = bq+r

=> 216 = 180×1+36

Let a = 180 and b = 36

On writing a = bq+r

=> 180 + 36×5+0

HCF (7344,1260) = 36

Answer:-

HCF of the two numbers 1260 and 7344 is 36

Used Method:-

Euclids Division Algorithm:-

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

Procedure:-

• Take the given numbers and divide the bigger by smaller and write the bigger number in the form of divisor×quotient+remainder.
• Take the divisor as a dividend and divide that number by remainder and do the same process until get the remainder as zero.
• The HCF of the two numbers by taking the divisor which gives the remainder is zero.