Highest Common Factor of 209, 910 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 209, 910 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 209, 910 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 209, 910 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 209, 910 is 1.

HCF(209, 910) = 1

HCF of 209, 910 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 209, 910 is 1.

Highest Common Factor of 209,910 using Euclid's algorithm

Highest Common Factor of 209,910 is 1

Step 1: Since 910 > 209, we apply the division lemma to 910 and 209, to get

910 = 209 x 4 + 74

Step 2: Since the reminder 209 ≠ 0, we apply division lemma to 74 and 209, to get

209 = 74 x 2 + 61

Step 3: We consider the new divisor 74 and the new remainder 61, and apply the division lemma to get

74 = 61 x 1 + 13

We consider the new divisor 61 and the new remainder 13,and apply the division lemma to get

61 = 13 x 4 + 9

We consider the new divisor 13 and the new remainder 9,and apply the division lemma to get

13 = 9 x 1 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 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 209 and 910 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(61,13) = HCF(74,61) = HCF(209,74) = HCF(910,209) .

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Frequently Asked Questions on HCF of 209, 910 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 209, 910?

Answer: HCF of 209, 910 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 209, 910 using Euclid's Algorithm?

Answer: For arbitrary numbers 209, 910 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.