Highest Common Factor of 6746, 4075 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 6746, 4075 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6746, 4075 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 6746, 4075 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 6746, 4075 is 1.

HCF(6746, 4075) = 1

HCF of 6746, 4075 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 6746, 4075 is 1.

Highest Common Factor of 6746,4075 using Euclid's algorithm

Highest Common Factor of 6746,4075 is 1

Step 1: Since 6746 > 4075, we apply the division lemma to 6746 and 4075, to get

6746 = 4075 x 1 + 2671

Step 2: Since the reminder 4075 ≠ 0, we apply division lemma to 2671 and 4075, to get

4075 = 2671 x 1 + 1404

Step 3: We consider the new divisor 2671 and the new remainder 1404, and apply the division lemma to get

2671 = 1404 x 1 + 1267

We consider the new divisor 1404 and the new remainder 1267,and apply the division lemma to get

1404 = 1267 x 1 + 137

We consider the new divisor 1267 and the new remainder 137,and apply the division lemma to get

1267 = 137 x 9 + 34

We consider the new divisor 137 and the new remainder 34,and apply the division lemma to get

137 = 34 x 4 + 1

We consider the new divisor 34 and the new remainder 1,and apply the division lemma to get

34 = 1 x 34 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6746 and 4075 is 1

Notice that 1 = HCF(34,1) = HCF(137,34) = HCF(1267,137) = HCF(1404,1267) = HCF(2671,1404) = HCF(4075,2671) = HCF(6746,4075) .

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Frequently Asked Questions on HCF of 6746, 4075 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 6746, 4075?

Answer: HCF of 6746, 4075 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6746, 4075 using Euclid's Algorithm?

Answer: For arbitrary numbers 6746, 4075 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.