HCF of 49, 62, 80, 117 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 49,62,80,117 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(49,62,80,117).

Here 62 is greater than 49

Now, consider the largest number as 'a' from the given number ie., 62 and 49 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 62 > 49, we apply the division lemma to 62 and 49, to get

62 = 49 x 1 + 13

Step 2: Since the reminder 49 ≠ 0, we apply division lemma to 13 and 49, to get

49 = 13 x 3 + 10

Step 3: We consider the new divisor 13 and the new remainder 10, and apply the division lemma to get

13 = 10 x 1 + 3

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

10 = 3 x 3 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 49 and 62 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(49,13) = HCF(62,49) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Here 80 is greater than 1

Now, consider the largest number as 'a' from the given number ie., 80 and 1 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

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

80 = 1 x 80 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 80 is 1

Notice that 1 = HCF(80,1) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Here 117 is greater than 1

Now, consider the largest number as 'a' from the given number ie., 117 and 1 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 117 > 1, we apply the division lemma to 117 and 1, to get

117 = 1 x 117 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 117 is 1

Notice that 1 = HCF(117,1) .

Therefore, HCF of 49,62,80,117 using Euclid's division lemma is 1.