HCF of 77, 91, 143 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 77,91,143 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(77,91,143).

Here 91 is greater than 77

Now, consider the largest number as 'a' from the given number ie., 91 and 77 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 91 > 77, we apply the division lemma to 91 and 77, to get

91 = 77 x 1 + 14

Step 2: Since the reminder 77 ≠ 0, we apply division lemma to 14 and 77, to get

77 = 14 x 5 + 7

Step 3: We consider the new divisor 14 and the new remainder 7, and apply the division lemma to get

14 = 7 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 77 and 91 is 7

Notice that 7 = HCF(14,7) = HCF(77,14) = HCF(91,77) .

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

Here 143 is greater than 7

Now, consider the largest number as 'a' from the given number ie., 143 and 7 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 143 > 7, we apply the division lemma to 143 and 7, to get

143 = 7 x 20 + 3

Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 3 and 7, to get

7 = 3 x 2 + 1

Step 3: 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 7 and 143 is 1

Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(143,7) .

Therefore, HCF of 77,91,143 using Euclid's division lemma is 1.