HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 63, 81, 108, 120 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 63, 81, 108, 120 is 3 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 63, 81, 108, 120 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 63, 81, 108, 120 is **3**.

HCF(63, 81, 108, 120) = 3

*Highest common factor* or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

Highest common factor (HCF) of 63, 81, 108, 120 is **3**.

**Step 1:** Since 81 > 63, we apply the division lemma to 81 and 63, to get

81 = 63 x 1 + 18

**Step 2:** Since the reminder 63 ≠ 0, we apply division lemma to 18 and 63, to get

63 = 18 x 3 + 9

**Step 3:** We consider the new divisor 18 and the new remainder 9, and apply the division lemma to get

18 = 9 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 63 and 81 is 9

Notice that 9 = HCF(18,9) = HCF(63,18) = HCF(81,63) .

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

**Step 1:** Since 108 > 9, we apply the division lemma to 108 and 9, to get

108 = 9 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 9 and 108 is 9

Notice that 9 = HCF(108,9) .

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

**Step 1:** Since 120 > 9, we apply the division lemma to 120 and 9, to get

120 = 9 x 13 + 3

**Step 2:** Since the reminder 9 ≠ 0, we apply division lemma to 3 and 9, to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9 and 120 is 3

Notice that 3 = HCF(9,3) = HCF(120,9) .

Here are some samples of HCF using Euclid's Algorithm calculations.

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 63, 81, 108, 120?

Answer: HCF of 63, 81, 108, 120 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 63, 81, 108, 120 using Euclid's Algorithm?

Answer: For arbitrary numbers 63, 81, 108, 120 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.