Highest Common Factor of 680, 708, 347 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 680, 708, 347 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 680, 708, 347 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 680, 708, 347 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 680, 708, 347 is 1.

HCF(680, 708, 347) = 1

HCF of 680, 708, 347 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 680, 708, 347 is 1.

Highest Common Factor of 680,708,347 using Euclid's algorithm

Highest Common Factor of 680,708,347 is 1

Step 1: Since 708 > 680, we apply the division lemma to 708 and 680, to get

708 = 680 x 1 + 28

Step 2: Since the reminder 680 ≠ 0, we apply division lemma to 28 and 680, to get

680 = 28 x 24 + 8

Step 3: We consider the new divisor 28 and the new remainder 8, and apply the division lemma to get

28 = 8 x 3 + 4

We consider the new divisor 8 and the new remainder 4, and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 680 and 708 is 4

Notice that 4 = HCF(8,4) = HCF(28,8) = HCF(680,28) = HCF(708,680) .

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

Step 1: Since 347 > 4, we apply the division lemma to 347 and 4, to get

347 = 4 x 86 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 347 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(347,4) .

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Frequently Asked Questions on HCF of 680, 708, 347 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 680, 708, 347?

Answer: HCF of 680, 708, 347 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 680, 708, 347 using Euclid's Algorithm?

Answer: For arbitrary numbers 680, 708, 347 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.