Highest Common Factor of 826, 614, 659 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 826, 614, 659 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 826, 614, 659 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 826, 614, 659 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 826, 614, 659 is 1.

HCF(826, 614, 659) = 1

HCF of 826, 614, 659 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 826, 614, 659 is 1.

Highest Common Factor of 826,614,659 using Euclid's algorithm

Highest Common Factor of 826,614,659 is 1

Step 1: Since 826 > 614, we apply the division lemma to 826 and 614, to get

826 = 614 x 1 + 212

Step 2: Since the reminder 614 ≠ 0, we apply division lemma to 212 and 614, to get

614 = 212 x 2 + 190

Step 3: We consider the new divisor 212 and the new remainder 190, and apply the division lemma to get

212 = 190 x 1 + 22

We consider the new divisor 190 and the new remainder 22,and apply the division lemma to get

190 = 22 x 8 + 14

We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get

22 = 14 x 1 + 8

We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get

14 = 8 x 1 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 826 and 614 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(190,22) = HCF(212,190) = HCF(614,212) = HCF(826,614) .

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

Step 1: Since 659 > 2, we apply the division lemma to 659 and 2, to get

659 = 2 x 329 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 659 is 1

Notice that 1 = HCF(2,1) = HCF(659,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 826, 614, 659 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 826, 614, 659?

Answer: HCF of 826, 614, 659 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 826, 614, 659 using Euclid's Algorithm?

Answer: For arbitrary numbers 826, 614, 659 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.