HCF of 28, 77, 91, 118 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 28,77,91,118 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(28,77,91,118).

Here 77 is greater than 28

Now, consider the largest number as 'a' from the given number ie., 77 and 28 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 77 > 28, we apply the division lemma to 77 and 28, to get

77 = 28 x 2 + 21

Step 2: Since the reminder 28 ≠ 0, we apply division lemma to 21 and 28, to get

28 = 21 x 1 + 7

Step 3: We consider the new divisor 21 and the new remainder 7, and apply the division lemma to get

21 = 7 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 28 and 77 is 7

Notice that 7 = HCF(21,7) = HCF(28,21) = HCF(77,28) .

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

Here 91 is greater than 7

Now, consider the largest number as 'a' from the given number ie., 91 and 7 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 91 > 7, we apply the division lemma to 91 and 7, to get

91 = 7 x 13 + 0

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

Notice that 7 = HCF(91,7) .

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

Here 118 is greater than 7

Now, consider the largest number as 'a' from the given number ie., 118 and 7 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 118 > 7, we apply the division lemma to 118 and 7, to get

118 = 7 x 16 + 6

Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 6 and 7, to get

7 = 6 x 1 + 1

Step 3: We consider the new divisor 6 and the new remainder 1, and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 118 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(118,7) .

Therefore, HCF of 28,77,91,118 using Euclid's division lemma is 1.