Question

Find the H.C.F. of 455 and 84 using division algorithm.

Answer 1

HCF of 455 and 84

divident = divisor * quotient + reminder

step 1- 455 = 84 * 5 + 35
step 2 - 84 = 35 * 2 + 14
step 3 - 35 = 14 * 2 + 7
step 3 - 14 = 7 * 2 + 0

thus HCF (455 , 84) = 7  ,,i.e, the last divisor.

Answer 2

Given: Two numbers 455 and 84

To find: The HCF of given numbers

Solution:

Using Euclid's division lemma 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 455 and smaller is 84

We need to apply Euclid's Division Lemma (a = bq + r) on the given numbers where a = 455 and b = 84.

We get,

⇒ 455 = 84 × 5 + 35

Now, we need to apply Euclid's Division Lemma again taking a = 84 and b = 35

⇒ 84 = 35 × 2 + 14

Taking a = 35 and b = 14

⇒ 35 = 14 × 2 + 7

Taking a = 14 and b = 7

⇒ 14 = 7 × 2 + 0

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

Now, the divisor is 7 when remainder is 0.

Hence, 7 is the HCF of 455 and 84.