Highest Common Factor of 208, 403 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 208, 403 i.e. 13 the largest integer that leaves a remainder zero for all numbers.

HCF of 208, 403 is 13 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 208, 403 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 208, 403 is 13.

HCF(208, 403) = 13

HCF of 208, 403 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 208, 403 is 13.

Highest Common Factor of 208,403 using Euclid's algorithm

Highest Common Factor of 208,403 is 13

Step 1: Since 403 > 208, we apply the division lemma to 403 and 208, to get

403 = 208 x 1 + 195

Step 2: Since the reminder 208 ≠ 0, we apply division lemma to 195 and 208, to get

208 = 195 x 1 + 13

Step 3: We consider the new divisor 195 and the new remainder 13, and apply the division lemma to get

195 = 13 x 15 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 208 and 403 is 13

Notice that 13 = HCF(195,13) = HCF(208,195) = HCF(403,208) .

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Frequently Asked Questions on HCF of 208, 403 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 208, 403?

Answer: HCF of 208, 403 is 13 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 208, 403 using Euclid's Algorithm?

Answer: For arbitrary numbers 208, 403 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.