HCF of 16, 32, 40 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 16,32,40 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(16,32,40).

Here 32 is greater than 16

Now, consider the largest number as 'a' from the given number ie., 32 and 16 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 32 > 16, we apply the division lemma to 32 and 16, 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 16 and 32 is 16

Notice that 16 = HCF(32,16) .

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

Here 40 is greater than 16

Now, consider the largest number as 'a' from the given number ie., 40 and 16 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 40 > 16, we apply the division lemma to 40 and 16, to get

40 = 16 x 2 + 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 40 is 8

Notice that 8 = HCF(16,8) = HCF(40,16) .

Therefore, HCF of 16,32,40 using Euclid's division lemma is 8.