Highest Common Factor of 207, 494 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 207, 494 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 207, 494 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 207, 494 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 207, 494 is 1.

HCF(207, 494) = 1

HCF of 207, 494 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 207, 494 is 1.

Highest Common Factor of 207,494 using Euclid's algorithm

Highest Common Factor of 207,494 is 1

Step 1: Since 494 > 207, we apply the division lemma to 494 and 207, to get

494 = 207 x 2 + 80

Step 2: Since the reminder 207 ≠ 0, we apply division lemma to 80 and 207, to get

207 = 80 x 2 + 47

Step 3: We consider the new divisor 80 and the new remainder 47, and apply the division lemma to get

80 = 47 x 1 + 33

We consider the new divisor 47 and the new remainder 33,and apply the division lemma to get

47 = 33 x 1 + 14

We consider the new divisor 33 and the new remainder 14,and apply the division lemma to get

33 = 14 x 2 + 5

We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get

14 = 5 x 2 + 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 207 and 494 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(33,14) = HCF(47,33) = HCF(80,47) = HCF(207,80) = HCF(494,207) .

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Frequently Asked Questions on HCF of 207, 494 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 207, 494?

Answer: HCF of 207, 494 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 207, 494 using Euclid's Algorithm?

Answer: For arbitrary numbers 207, 494 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.