HCF of 21, 40, 84, 98 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 21,40,84,98 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(21,40,84,98).

Here 40 is greater than 21

Now, consider the largest number as 'a' from the given number ie., 40 and 21 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 40 > 21, we apply the division lemma to 40 and 21, to get

40 = 21 x 1 + 19

Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 19 and 21, to get

21 = 19 x 1 + 2

Step 3: We consider the new divisor 19 and the new remainder 2, and apply the division lemma to get

19 = 2 x 9 + 1

We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 21 and 40 is 1

Notice that 1 = HCF(2,1) = HCF(19,2) = HCF(21,19) = HCF(40,21) .

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

Here 84 is greater than 1

Now, consider the largest number as 'a' from the given number ie., 84 and 1 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 84 > 1, we apply the division lemma to 84 and 1, to get

84 = 1 x 84 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 84 is 1

Notice that 1 = HCF(84,1) .

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

Here 98 is greater than 1

Now, consider the largest number as 'a' from the given number ie., 98 and 1 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 98 > 1, we apply the division lemma to 98 and 1, to get

98 = 1 x 98 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 98 is 1

Notice that 1 = HCF(98,1) .

Therefore, HCF of 21,40,84,98 using Euclid's division lemma is 1.