HCF of 15, 35, 42, 68 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 15,35,42,68 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(15,35,42,68).

Here 35 is greater than 15

Now, consider the largest number as 'a' from the given number ie., 35 and 15 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 35 > 15, we apply the division lemma to 35 and 15, to get

35 = 15 x 2 + 5

Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 5 and 15, to get

15 = 5 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 15 and 35 is 5

Notice that 5 = HCF(15,5) = HCF(35,15) .

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

Here 42 is greater than 5

Now, consider the largest number as 'a' from the given number ie., 42 and 5 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 42 > 5, we apply the division lemma to 42 and 5, to get

42 = 5 x 8 + 2

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get

5 = 2 x 2 + 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 5 and 42 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(42,5) .

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

Here 68 is greater than 1

Now, consider the largest number as 'a' from the given number ie., 68 and 1 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 68 > 1, we apply the division lemma to 68 and 1, to get

68 = 1 x 68 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 68 is 1

Notice that 1 = HCF(68,1) .

Therefore, HCF of 15,35,42,68 using Euclid's division lemma is 1.