Highest Common Factor of 722, 422, 213 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 722, 422, 213 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 722, 422, 213 is 1 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 722, 422, 213 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 722, 422, 213 is 1.

HCF(722, 422, 213) = 1

HCF of 722, 422, 213 using Euclid's algorithm

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

HCF of:

Highest common factor (HCF) of 722, 422, 213 is 1.

Highest Common Factor of 722,422,213 using Euclid's algorithm

Highest Common Factor of 722,422,213 is 1

Step 1: Since 722 > 422, we apply the division lemma to 722 and 422, to get

722 = 422 x 1 + 300

Step 2: Since the reminder 422 ≠ 0, we apply division lemma to 300 and 422, to get

422 = 300 x 1 + 122

Step 3: We consider the new divisor 300 and the new remainder 122, and apply the division lemma to get

300 = 122 x 2 + 56

We consider the new divisor 122 and the new remainder 56,and apply the division lemma to get

122 = 56 x 2 + 10

We consider the new divisor 56 and the new remainder 10,and apply the division lemma to get

56 = 10 x 5 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 722 and 422 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(56,10) = HCF(122,56) = HCF(300,122) = HCF(422,300) = HCF(722,422) .

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

Step 1: Since 213 > 2, we apply the division lemma to 213 and 2, to get

213 = 2 x 106 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 213 is 1

Notice that 1 = HCF(2,1) = HCF(213,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 722, 422, 213 using Euclid's Algorithm

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 722, 422, 213?

Answer: HCF of 722, 422, 213 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 722, 422, 213 using Euclid's Algorithm?

Answer: For arbitrary numbers 722, 422, 213 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.