HCF of 240, 260, 370 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 240,260,370 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(240,260,370).

Here 260 is greater than 240

Now, consider the largest number as 'a' from the given number ie., 260 and 240 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 260 > 240, we apply the division lemma to 260 and 240, to get

260 = 240 x 1 + 20

Step 2: Since the reminder 240 ≠ 0, we apply division lemma to 20 and 240, to get

240 = 20 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 240 and 260 is 20

Notice that 20 = HCF(240,20) = HCF(260,240) .

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

Here 370 is greater than 20

Now, consider the largest number as 'a' from the given number ie., 370 and 20 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 370 > 20, we apply the division lemma to 370 and 20, to get

370 = 20 x 18 + 10

Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 10 and 20, to get

20 = 10 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 20 and 370 is 10

Notice that 10 = HCF(20,10) = HCF(370,20) .

Therefore, HCF of 240,260,370 using Euclid's division lemma is 10.