HCF of 42, 21, 46 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 42,21,46 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(42,21,46).

Here 42 is greater than 21

Now, consider the largest number as 'a' from the given number ie., 42 and 21 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 42 > 21, we apply the division lemma to 42 and 21, to get

42 = 21 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 42 and 21 is 21

Notice that 21 = HCF(42,21) .

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

Here 46 is greater than 21

Now, consider the largest number as 'a' from the given number ie., 46 and 21 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 46 > 21, we apply the division lemma to 46 and 21, to get

46 = 21 x 2 + 4

Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 4 and 21, to get

21 = 4 x 5 + 1

Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 21 and 46 is 1

Notice that 1 = HCF(4,1) = HCF(21,4) = HCF(46,21) .

Therefore, HCF of 42,21,46 using Euclid's division lemma is 1.