HCF of 32, 48, 56 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 32,48,56 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(32,48,56).

Here 48 is greater than 32

Now, consider the largest number as 'a' from the given number ie., 48 and 32 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 48 > 32, we apply the division lemma to 48 and 32, to get

48 = 32 x 1 + 16

Step 2: Since the reminder 32 ≠ 0, we apply division lemma to 16 and 32, to get

32 = 16 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 32 and 48 is 16

Notice that 16 = HCF(32,16) = HCF(48,32) .

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

Here 56 is greater than 16

Now, consider the largest number as 'a' from the given number ie., 56 and 16 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 56 > 16, we apply the division lemma to 56 and 16, to get

56 = 16 x 3 + 8

Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 8 and 16, to get

16 = 8 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 16 and 56 is 8

Notice that 8 = HCF(16,8) = HCF(56,16) .

Therefore, HCF of 32,48,56 using Euclid's division lemma is 8.