Highest Common Factor of 6725, 4178 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 6725, 4178 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6725, 4178 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 6725, 4178 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 6725, 4178 is 1.

HCF(6725, 4178) = 1

HCF of 6725, 4178 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 6725, 4178 is 1.

Highest Common Factor of 6725,4178 using Euclid's algorithm

Highest Common Factor of 6725,4178 is 1

Step 1: Since 6725 > 4178, we apply the division lemma to 6725 and 4178, to get

6725 = 4178 x 1 + 2547

Step 2: Since the reminder 4178 ≠ 0, we apply division lemma to 2547 and 4178, to get

4178 = 2547 x 1 + 1631

Step 3: We consider the new divisor 2547 and the new remainder 1631, and apply the division lemma to get

2547 = 1631 x 1 + 916

We consider the new divisor 1631 and the new remainder 916,and apply the division lemma to get

1631 = 916 x 1 + 715

We consider the new divisor 916 and the new remainder 715,and apply the division lemma to get

916 = 715 x 1 + 201

We consider the new divisor 715 and the new remainder 201,and apply the division lemma to get

715 = 201 x 3 + 112

We consider the new divisor 201 and the new remainder 112,and apply the division lemma to get

201 = 112 x 1 + 89

We consider the new divisor 112 and the new remainder 89,and apply the division lemma to get

112 = 89 x 1 + 23

We consider the new divisor 89 and the new remainder 23,and apply the division lemma to get

89 = 23 x 3 + 20

We consider the new divisor 23 and the new remainder 20,and apply the division lemma to get

23 = 20 x 1 + 3

We consider the new divisor 20 and the new remainder 3,and apply the division lemma to get

20 = 3 x 6 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 6725 and 4178 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(20,3) = HCF(23,20) = HCF(89,23) = HCF(112,89) = HCF(201,112) = HCF(715,201) = HCF(916,715) = HCF(1631,916) = HCF(2547,1631) = HCF(4178,2547) = HCF(6725,4178) .

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Frequently Asked Questions on HCF of 6725, 4178 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 6725, 4178?

Answer: HCF of 6725, 4178 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6725, 4178 using Euclid's Algorithm?

Answer: For arbitrary numbers 6725, 4178 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.