HCF of 945, 540, 560 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 945,540,560 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(945,540,560).

Here 945 is greater than 540

Now, consider the largest number as 'a' from the given number ie., 945 and 540 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 945 > 540, we apply the division lemma to 945 and 540, to get

945 = 540 x 1 + 405

Step 2: Since the reminder 540 ≠ 0, we apply division lemma to 405 and 540, to get

540 = 405 x 1 + 135

Step 3: We consider the new divisor 405 and the new remainder 135, and apply the division lemma to get

405 = 135 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 135, the HCF of 945 and 540 is 135

Notice that 135 = HCF(405,135) = HCF(540,405) = HCF(945,540) .

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

Here 560 is greater than 135

Now, consider the largest number as 'a' from the given number ie., 560 and 135 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 560 > 135, we apply the division lemma to 560 and 135, to get

560 = 135 x 4 + 20

Step 2: Since the reminder 135 ≠ 0, we apply division lemma to 20 and 135, to get

135 = 20 x 6 + 15

Step 3: We consider the new divisor 20 and the new remainder 15, and apply the division lemma to get

20 = 15 x 1 + 5

We consider the new divisor 15 and the new remainder 5, and apply the division lemma 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 135 and 560 is 5

Notice that 5 = HCF(15,5) = HCF(20,15) = HCF(135,20) = HCF(560,135) .

Therefore, HCF of 945,540,560 using Euclid's division lemma is 5.