Question

use the euclid's division algorithm to find the HCF of 2710 and 55.
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Answer 1

Answer:

Hi frnd........

Step-by-step explanation:

By Euclids division lemma,

2710=55×49+15

Again by euclids division lemma,

55=15×3+10

Again by euclids division lemma,

15=10×1+5

Again by euclids division lemma,

10=5×2+0

HCF =5

Answer 2

Given: Two numbers 2710 and 55

To find: The HCF of given numbers

Solution:

(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 2710 and smaller is 55

We need to apply Euclid's Division Lemma (a = bq + r) on the given numbers where a = 2710 and b = 55.

We get,

⇒ 2710 = 55 × 49 + 15

Now, we need to apply Euclid's Division Lemma again taking a = 55 and b = 15

⇒ 55 = 15 × 3 + 10

Taking a = 15 and b = 10

⇒ 15 = 10 × 1 + 5

Taking a = 10 and b = 5

⇒ 10 = 5 × 2 + 0

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

Now, the divisor is 5 when remainder is 0.

Hence, 5 is the HCF of 2710 and 55.