HCF of 21, 30, 44 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 21,30,44 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(21,30,44).

Here 30 is greater than 21

Now, consider the largest number as 'a' from the given number ie., 30 and 21 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 30 > 21, we apply the division lemma to 30 and 21, to get

30 = 21 x 1 + 9

Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 9 and 21, to get

21 = 9 x 2 + 3

Step 3: We consider the new divisor 9 and the new remainder 3, and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 21 and 30 is 3

Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(30,21) .

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

Here 44 is greater than 3

Now, consider the largest number as 'a' from the given number ie., 44 and 3 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 44 > 3, we apply the division lemma to 44 and 3, to get

44 = 3 x 14 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 44 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(44,3) .

Therefore, HCF of 21,30,44 using Euclid's division lemma is 1.