Question

HCF of 42 and 80 by Euclid's lemma​

Answer 1

ANSWER :

Highest common factor (HCF) of 42, 80 is 2.

STEP BY STEP EXPLAINATION :

Here 80 is greater than 42

Now, consider the largest number as 'a' from the given number ie., 80 and 42 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 80 > 42, we apply the division lemma to 80 and 42, to get

80 = 42 x 1 + 38

Step 2: Since the reminder 42 ≠ 0, we apply division lemma to 38 and 42, to get

42 = 38 x 1 + 4

Step 3: We consider the new divisor 38 and the new remainder 4, and apply the division lemma to get

38 = 4 x 9 + 2

We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 42 and 80 is 2

Notice that 2 = HCF(4,2) = HCF(38,4) = HCF(42,38) = HCF(80,42) .

Therefore, HCF of 42,80 using Euclid's division lemma is 2.