Highest Common Factor of 213, 561, 209 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 213, 561, 209 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 213, 561, 209 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 213, 561, 209 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 213, 561, 209 is 1.

HCF(213, 561, 209) = 1

HCF of 213, 561, 209 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 213, 561, 209 is 1.

Highest Common Factor of 213,561,209 using Euclid's algorithm

Highest Common Factor of 213,561,209 is 1

Step 1: Since 561 > 213, we apply the division lemma to 561 and 213, to get

561 = 213 x 2 + 135

Step 2: Since the reminder 213 ≠ 0, we apply division lemma to 135 and 213, to get

213 = 135 x 1 + 78

Step 3: We consider the new divisor 135 and the new remainder 78, and apply the division lemma to get

135 = 78 x 1 + 57

We consider the new divisor 78 and the new remainder 57,and apply the division lemma to get

78 = 57 x 1 + 21

We consider the new divisor 57 and the new remainder 21,and apply the division lemma to get

57 = 21 x 2 + 15

We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get

21 = 15 x 1 + 6

We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get

15 = 6 x 2 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 213 and 561 is 3

Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(57,21) = HCF(78,57) = HCF(135,78) = HCF(213,135) = HCF(561,213) .

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

Step 1: Since 209 > 3, we apply the division lemma to 209 and 3, to get

209 = 3 x 69 + 2

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

3 = 2 x 1 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 3 and 209 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(209,3) .

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Frequently Asked Questions on HCF of 213, 561, 209 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 213, 561, 209?

Answer: HCF of 213, 561, 209 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 213, 561, 209 using Euclid's Algorithm?

Answer: For arbitrary numbers 213, 561, 209 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.