HCF of 24, 32, 52, 72 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 24,32,52,72 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(24,32,52,72).

Here 32 is greater than 24

Now, consider the largest number as 'a' from the given number ie., 32 and 24 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 32 > 24, we apply the division lemma to 32 and 24, to get

32 = 24 x 1 + 8

Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 8 and 24, to get

24 = 8 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 24 and 32 is 8

Notice that 8 = HCF(24,8) = HCF(32,24) .

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

Here 52 is greater than 8

Now, consider the largest number as 'a' from the given number ie., 52 and 8 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 52 > 8, we apply the division lemma to 52 and 8, to get

52 = 8 x 6 + 4

Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 4 and 8, to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 8 and 52 is 4

Notice that 4 = HCF(8,4) = HCF(52,8) .

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

Here 72 is greater than 4

Now, consider the largest number as 'a' from the given number ie., 72 and 4 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 72 > 4, we apply the division lemma to 72 and 4, to get

72 = 4 x 18 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 72 is 4

Notice that 4 = HCF(72,4) .

Therefore, HCF of 24,32,52,72 using Euclid's division lemma is 4.