Highest Common Factor of 642, 710, 569 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 642, 710, 569 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 642, 710, 569 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 642, 710, 569 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 642, 710, 569 is 1.

HCF(642, 710, 569) = 1

HCF of 642, 710, 569 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 642, 710, 569 is 1.

Highest Common Factor of 642,710,569 using Euclid's algorithm

Highest Common Factor of 642,710,569 is 1

Step 1: Since 710 > 642, we apply the division lemma to 710 and 642, to get

710 = 642 x 1 + 68

Step 2: Since the reminder 642 ≠ 0, we apply division lemma to 68 and 642, to get

642 = 68 x 9 + 30

Step 3: We consider the new divisor 68 and the new remainder 30, and apply the division lemma to get

68 = 30 x 2 + 8

We consider the new divisor 30 and the new remainder 8,and apply the division lemma to get

30 = 8 x 3 + 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 642 and 710 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(30,8) = HCF(68,30) = HCF(642,68) = HCF(710,642) .

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

Step 1: Since 569 > 2, we apply the division lemma to 569 and 2, to get

569 = 2 x 284 + 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 569 is 1

Notice that 1 = HCF(2,1) = HCF(569,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 642, 710, 569 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 642, 710, 569?

Answer: HCF of 642, 710, 569 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 642, 710, 569 using Euclid's Algorithm?

Answer: For arbitrary numbers 642, 710, 569 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.