HCF of 48, 72, 90 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 48,72,90 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(48,72,90).

Here 72 is greater than 48

Now, consider the largest number as 'a' from the given number ie., 72 and 48 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 72 > 48, we apply the division lemma to 72 and 48, to get

72 = 48 x 1 + 24

Step 2: Since the reminder 48 ≠ 0, we apply division lemma to 24 and 48, to get

48 = 24 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 48 and 72 is 24

Notice that 24 = HCF(48,24) = HCF(72,48) .

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

Here 90 is greater than 24

Now, consider the largest number as 'a' from the given number ie., 90 and 24 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 90 > 24, we apply the division lemma to 90 and 24, to get

90 = 24 x 3 + 18

Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 18 and 24, to get

24 = 18 x 1 + 6

Step 3: We consider the new divisor 18 and the new remainder 6, and apply the division lemma to get

18 = 6 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 24 and 90 is 6

Notice that 6 = HCF(18,6) = HCF(24,18) = HCF(90,24) .

Therefore, HCF of 48,72,90 using Euclid's division lemma is 6.