Highest Common Factor of 65, 429, 686 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 65, 429, 686 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 65, 429, 686 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 65, 429, 686 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 65, 429, 686 is 1.

HCF(65, 429, 686) = 1

HCF of 65, 429, 686 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 65, 429, 686 is 1.

Highest Common Factor of 65,429,686 using Euclid's algorithm

Highest Common Factor of 65,429,686 is 1

Step 1: Since 429 > 65, we apply the division lemma to 429 and 65, to get

429 = 65 x 6 + 39

Step 2: Since the reminder 65 ≠ 0, we apply division lemma to 39 and 65, to get

65 = 39 x 1 + 26

Step 3: We consider the new divisor 39 and the new remainder 26, and apply the division lemma to get

39 = 26 x 1 + 13

We consider the new divisor 26 and the new remainder 13, and apply the division lemma to get

26 = 13 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 65 and 429 is 13

Notice that 13 = HCF(26,13) = HCF(39,26) = HCF(65,39) = HCF(429,65) .

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

Step 1: Since 686 > 13, we apply the division lemma to 686 and 13, to get

686 = 13 x 52 + 10

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 10 and 13, to get

13 = 10 x 1 + 3

Step 3: We consider the new divisor 10 and the new remainder 3, and apply the division lemma to get

10 = 3 x 3 + 1

We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 13 and 686 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(686,13) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 65, 429, 686 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 65, 429, 686?

Answer: HCF of 65, 429, 686 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 65, 429, 686 using Euclid's Algorithm?

Answer: For arbitrary numbers 65, 429, 686 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.