HCF of 28, 42, 49 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 28,42,49 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(28,42,49).

Here 42 is greater than 28

Now, consider the largest number as 'a' from the given number ie., 42 and 28 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 42 > 28, we apply the division lemma to 42 and 28, to get

42 = 28 x 1 + 14

Step 2: Since the reminder 28 ≠ 0, we apply division lemma to 14 and 28, to get

28 = 14 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 28 and 42 is 14

Notice that 14 = HCF(28,14) = HCF(42,28) .

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

Here 49 is greater than 14

Now, consider the largest number as 'a' from the given number ie., 49 and 14 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 49 > 14, we apply the division lemma to 49 and 14, to get

49 = 14 x 3 + 7

Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 7 and 14, 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 14 and 49 is 7

Notice that 7 = HCF(14,7) = HCF(49,14) .

Therefore, HCF of 28,42,49 using Euclid's division lemma is 7.