HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 9, 12, 21 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 9, 12, 21 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 9, 12, 21 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 9, 12, 21 is **3**.

HCF(9, 12, 21) = 3

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

Highest common factor (HCF) of 9, 12, 21 is **3**.

**Step 1:** Since 12 > 9, we apply the division lemma to 12 and 9, to get

12 = 9 x 1 + 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 12 is 3

Notice that 3 = HCF(9,3) = HCF(12,9) .

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

**Step 1:** Since 21 > 3, we apply the division lemma to 21 and 3, to get

21 = 3 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 21 is 3

Notice that 3 = HCF(21,3) .

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 9, 12, 21?

Answer: HCF of 9, 12, 21 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9, 12, 21 using Euclid's Algorithm?

Answer: For arbitrary numbers 9, 12, 21 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.