Question

.Find the H.C.F of 62 and 114

Answer 1

Find the prime factorization of 62

62 = 2 × 31

Find the prime factorization of 114

114 = 2 × 3 × 19

To find the GCF, multiply all the prime factors common to both numbers:

Therefore, GCF = 2

Answer 2

Answer:

The HCF of 62 and 114 is 2.

Step-by-step explanation:

Here 114 is greater than 62

Now, consider the largest number as 'a' from the given number ie., 114 and 62 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 114 > 62, we apply the division lemma to 114 and 62, to get

114 = 62 x 1 + 52

Step 2: Since the reminder 62 ≠ 0, we apply division lemma to 52 and 62, to get

62 = 52 x 1 + 10

Step 3: We consider the new divisor 52 and the new remainder 10, and apply the division lemma to get

52 = 10 x 5 + 2

We consider the new divisor 10 and the new remainder 2, and apply the division lemma to get

10 = 2 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 114 and 62 is 2

Notice that 2 = HCF(10,2) = HCF(52,10) = HCF(62,52) = HCF(114,62) .

Therefore, HCF of 114,62 using Euclid's division lemma is 2.