Highest Common Factor of 6843, 6508, 37314 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 6843, 6508, 37314 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6843, 6508, 37314 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 6843, 6508, 37314 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 6843, 6508, 37314 is 1.

HCF(6843, 6508, 37314) = 1

HCF of 6843, 6508, 37314 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 6843, 6508, 37314 is 1.

Highest Common Factor of 6843,6508,37314 using Euclid's algorithm

Highest Common Factor of 6843,6508,37314 is 1

Step 1: Since 6843 > 6508, we apply the division lemma to 6843 and 6508, to get

6843 = 6508 x 1 + 335

Step 2: Since the reminder 6508 ≠ 0, we apply division lemma to 335 and 6508, to get

6508 = 335 x 19 + 143

Step 3: We consider the new divisor 335 and the new remainder 143, and apply the division lemma to get

335 = 143 x 2 + 49

We consider the new divisor 143 and the new remainder 49,and apply the division lemma to get

143 = 49 x 2 + 45

We consider the new divisor 49 and the new remainder 45,and apply the division lemma to get

49 = 45 x 1 + 4

We consider the new divisor 45 and the new remainder 4,and apply the division lemma to get

45 = 4 x 11 + 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 6843 and 6508 is 1

Notice that 1 = HCF(4,1) = HCF(45,4) = HCF(49,45) = HCF(143,49) = HCF(335,143) = HCF(6508,335) = HCF(6843,6508) .

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

Step 1: Since 37314 > 1, we apply the division lemma to 37314 and 1, to get

37314 = 1 x 37314 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 37314 is 1

Notice that 1 = HCF(37314,1) .

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Frequently Asked Questions on HCF of 6843, 6508, 37314 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 6843, 6508, 37314?

Answer: HCF of 6843, 6508, 37314 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6843, 6508, 37314 using Euclid's Algorithm?

Answer: For arbitrary numbers 6843, 6508, 37314 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.