HCF of 16, 36, 80, 100 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 16,36,80,100 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(16,36,80,100).

Here 36 is greater than 16

Now, consider the largest number as 'a' from the given number ie., 36 and 16 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 36 > 16, we apply the division lemma to 36 and 16, to get

36 = 16 x 2 + 4

Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 4 and 16, to get

16 = 4 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 16 and 36 is 4

Notice that 4 = HCF(16,4) = HCF(36,16) .

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

Here 80 is greater than 4

Now, consider the largest number as 'a' from the given number ie., 80 and 4 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 80 > 4, we apply the division lemma to 80 and 4, to get

80 = 4 x 20 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 80 is 4

Notice that 4 = HCF(80,4) .

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

Here 100 is greater than 4

Now, consider the largest number as 'a' from the given number ie., 100 and 4 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 100 > 4, we apply the division lemma to 100 and 4, to get

100 = 4 x 25 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 100 is 4

Notice that 4 = HCF(100,4) .

Therefore, HCF of 16,36,80,100 using Euclid's division lemma is 4.