HCF of 60, 84, 140 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 60,84,140 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(60,84,140).

Here 84 is greater than 60

Now, consider the largest number as 'a' from the given number ie., 84 and 60 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 84 > 60, we apply the division lemma to 84 and 60, to get

84 = 60 x 1 + 24

Step 2: Since the reminder 60 ≠ 0, we apply division lemma to 24 and 60, to get

60 = 24 x 2 + 12

Step 3: We consider the new divisor 24 and the new remainder 12, and apply the division lemma to get

24 = 12 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 60 and 84 is 12

Notice that 12 = HCF(24,12) = HCF(60,24) = HCF(84,60) .

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

Here 140 is greater than 12

Now, consider the largest number as 'a' from the given number ie., 140 and 12 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 140 > 12, we apply the division lemma to 140 and 12, to get

140 = 12 x 11 + 8

Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 8 and 12, to get

12 = 8 x 1 + 4

Step 3: We consider the new divisor 8 and the new remainder 4, and apply the division lemma 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 12 and 140 is 4

Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(140,12) .

Therefore, HCF of 60,84,140 using Euclid's division lemma is 4.