HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 108, 120, 144 i.e. 12 the largest integer that leaves a remainder zero for all numbers.

HCF of 108, 120, 144 is 12 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 108, 120, 144 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 108, 120, 144 is **12**.

HCF(108, 120, 144) = 12

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

Highest common factor (HCF) of 108, 120, 144 is **12**.

**Step 1:** Since 120 > 108, we apply the division lemma to 120 and 108, to get

120 = 108 x 1 + 12

**Step 2:** Since the reminder 108 ≠ 0, we apply division lemma to 12 and 108, to get

108 = 12 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 108 and 120 is 12

Notice that 12 = HCF(108,12) = HCF(120,108) .

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

**Step 1:** Since 144 > 12, we apply the division lemma to 144 and 12, to get

144 = 12 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 12 and 144 is 12

Notice that 12 = HCF(144,12) .

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 108, 120, 144?

Answer: HCF of 108, 120, 144 is 12 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 108, 120, 144 using Euclid's Algorithm?

Answer: For arbitrary numbers 108, 120, 144 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.