Highest Common Factor of 506, 714, 206 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 506, 714, 206 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 506, 714, 206 is 2 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 506, 714, 206 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 506, 714, 206 is 2.

HCF(506, 714, 206) = 2

HCF of 506, 714, 206 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 506, 714, 206 is 2.

Highest Common Factor of 506,714,206 using Euclid's algorithm

Highest Common Factor of 506,714,206 is 2

Step 1: Since 714 > 506, we apply the division lemma to 714 and 506, to get

714 = 506 x 1 + 208

Step 2: Since the reminder 506 ≠ 0, we apply division lemma to 208 and 506, to get

506 = 208 x 2 + 90

Step 3: We consider the new divisor 208 and the new remainder 90, and apply the division lemma to get

208 = 90 x 2 + 28

We consider the new divisor 90 and the new remainder 28,and apply the division lemma to get

90 = 28 x 3 + 6

We consider the new divisor 28 and the new remainder 6,and apply the division lemma to get

28 = 6 x 4 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 506 and 714 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(28,6) = HCF(90,28) = HCF(208,90) = HCF(506,208) = HCF(714,506) .

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

Step 1: Since 206 > 2, we apply the division lemma to 206 and 2, to get

206 = 2 x 103 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 206 is 2

Notice that 2 = HCF(206,2) .

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Frequently Asked Questions on HCF of 506, 714, 206 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 506, 714, 206?

Answer: HCF of 506, 714, 206 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 506, 714, 206 using Euclid's Algorithm?

Answer: For arbitrary numbers 506, 714, 206 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.