Question

Find hcf of 867 and 225 by euclids division algorithm

Answer 1

Answer:3

Step-by-step explanation:

867 is grater then 225

867=225×3+192

225=192×1+33

192=33×5+27

33=27×1+6

27=6×4+3

6=3×2+0

Therefore HCF of 867 and 225 = 3

Answer 2

Given: Two numbers 867 and 225

To find: The HCF of given numbers

Solution:

Using Euclid's division algorithm to find the HCF.

(Definition - According to Euclid's division lemma, if we have two positive integers a and b, then there exist unique integers q an r which satisfies the condition a = bq + r where 0 ≤ r < b)

Here, the greater integer is 867 and smaller is 225

We need to apply Euclid's Division Lemma (a = bq + r) on the given numbers where a = 867 and b = 225.

We get,

⇒ 867 = 225 × 3 + 192

Now, we need to apply Euclid's Division Lemma again taking a = 225 and b = 192

⇒ 225 = 192 × 1 + 33

Taking a = 192 and b = 33

⇒ 192 = 33 × 5 + 27

Taking a = 33 and b = 27

⇒ 33 = 27 × 1 + 6

Taking a = 27 and b =  6

⇒ 27 = 6 × 4 + 3

Taking a = 6 and b = 3

⇒ 6 = 3 × 2 + 0

As the remainder has become 0, we can't proceed further.

Now, the divisor is 3 when remainder is 0.

Hence, 3 is the HCF of 867 and 225.