Highest Common Factor of 5800, 3657, 70668 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 5800, 3657, 70668 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 5800, 3657, 70668 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 5800, 3657, 70668 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 5800, 3657, 70668 is 1.

HCF(5800, 3657, 70668) = 1

HCF of 5800, 3657, 70668 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 5800, 3657, 70668 is 1.

Highest Common Factor of 5800,3657,70668 using Euclid's algorithm

Highest Common Factor of 5800,3657,70668 is 1

Step 1: Since 5800 > 3657, we apply the division lemma to 5800 and 3657, to get

5800 = 3657 x 1 + 2143

Step 2: Since the reminder 3657 ≠ 0, we apply division lemma to 2143 and 3657, to get

3657 = 2143 x 1 + 1514

Step 3: We consider the new divisor 2143 and the new remainder 1514, and apply the division lemma to get

2143 = 1514 x 1 + 629

We consider the new divisor 1514 and the new remainder 629,and apply the division lemma to get

1514 = 629 x 2 + 256

We consider the new divisor 629 and the new remainder 256,and apply the division lemma to get

629 = 256 x 2 + 117

We consider the new divisor 256 and the new remainder 117,and apply the division lemma to get

256 = 117 x 2 + 22

We consider the new divisor 117 and the new remainder 22,and apply the division lemma to get

117 = 22 x 5 + 7

We consider the new divisor 22 and the new remainder 7,and apply the division lemma to get

22 = 7 x 3 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5800 and 3657 is 1

Notice that 1 = HCF(7,1) = HCF(22,7) = HCF(117,22) = HCF(256,117) = HCF(629,256) = HCF(1514,629) = HCF(2143,1514) = HCF(3657,2143) = HCF(5800,3657) .

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

Step 1: Since 70668 > 1, we apply the division lemma to 70668 and 1, to get

70668 = 1 x 70668 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 70668 is 1

Notice that 1 = HCF(70668,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 5800, 3657, 70668 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 5800, 3657, 70668?

Answer: HCF of 5800, 3657, 70668 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5800, 3657, 70668 using Euclid's Algorithm?

Answer: For arbitrary numbers 5800, 3657, 70668 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.