HCF of 40, 48, 60, 95 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 40,48,60,95 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(40,48,60,95).

Here 48 is greater than 40

Now, consider the largest number as 'a' from the given number ie., 48 and 40 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 48 > 40, we apply the division lemma to 48 and 40, to get

48 = 40 x 1 + 8

Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 8 and 40, to get

40 = 8 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 40 and 48 is 8

Notice that 8 = HCF(40,8) = HCF(48,40) .

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

Here 60 is greater than 8

Now, consider the largest number as 'a' from the given number ie., 60 and 8 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 60 > 8, we apply the division lemma to 60 and 8, to get

60 = 8 x 7 + 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 60 is 4

Notice that 4 = HCF(8,4) = HCF(60,8) .

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

Here 95 is greater than 4

Now, consider the largest number as 'a' from the given number ie., 95 and 4 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 95 > 4, we apply the division lemma to 95 and 4, to get

95 = 4 x 23 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

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

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 95 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(95,4) .

Therefore, HCF of 40,48,60,95 using Euclid's division lemma is 1.