Highest Common Factor of 686, 243, 708 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 686, 243, 708 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 686, 243, 708 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 686, 243, 708 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 686, 243, 708 is 1.

HCF(686, 243, 708) = 1

HCF of 686, 243, 708 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 686, 243, 708 is 1.

Highest Common Factor of 686,243,708 using Euclid's algorithm

Highest Common Factor of 686,243,708 is 1

Step 1: Since 686 > 243, we apply the division lemma to 686 and 243, to get

686 = 243 x 2 + 200

Step 2: Since the reminder 243 ≠ 0, we apply division lemma to 200 and 243, to get

243 = 200 x 1 + 43

Step 3: We consider the new divisor 200 and the new remainder 43, and apply the division lemma to get

200 = 43 x 4 + 28

We consider the new divisor 43 and the new remainder 28,and apply the division lemma to get

43 = 28 x 1 + 15

We consider the new divisor 28 and the new remainder 15,and apply the division lemma to get

28 = 15 x 1 + 13

We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get

15 = 13 x 1 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 686 and 243 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(28,15) = HCF(43,28) = HCF(200,43) = HCF(243,200) = HCF(686,243) .

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

Step 1: Since 708 > 1, we apply the division lemma to 708 and 1, to get

708 = 1 x 708 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 708 is 1

Notice that 1 = HCF(708,1) .

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Frequently Asked Questions on HCF of 686, 243, 708 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 686, 243, 708?

Answer: HCF of 686, 243, 708 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 686, 243, 708 using Euclid's Algorithm?

Answer: For arbitrary numbers 686, 243, 708 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.