Highest Common Factor of 338, 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 338, 213 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 338, 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 338, 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 338, 213 is 1.

HCF(338, 213) = 1

HCF of 338, 213 using Euclid's algorithm

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

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Highest common factor (HCF) of 338, 213 is 1.

Highest Common Factor of 338,213 using Euclid's algorithm

Highest Common Factor of 338,213 is 1

Step 1: Since 338 > 213, we apply the division lemma to 338 and 213, to get

338 = 213 x 1 + 125

Step 2: Since the reminder 213 ≠ 0, we apply division lemma to 125 and 213, to get

213 = 125 x 1 + 88

Step 3: We consider the new divisor 125 and the new remainder 88, and apply the division lemma to get

125 = 88 x 1 + 37

We consider the new divisor 88 and the new remainder 37,and apply the division lemma to get

88 = 37 x 2 + 14

We consider the new divisor 37 and the new remainder 14,and apply the division lemma to get

37 = 14 x 2 + 9

We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get

14 = 9 x 1 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 338 and 213 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(37,14) = HCF(88,37) = HCF(125,88) = HCF(213,125) = HCF(338,213) .

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Frequently Asked Questions on HCF of 338, 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 338, 213?

Answer: HCF of 338, 213 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 338, 213 using Euclid's Algorithm?

Answer: For arbitrary numbers 338, 213 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.