Highest Common Factor of 580, 666, 667 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 580, 666, 667 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 580, 666, 667 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 580, 666, 667 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 580, 666, 667 is 1.

HCF(580, 666, 667) = 1

HCF of 580, 666, 667 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 580, 666, 667 is 1.

Highest Common Factor of 580,666,667 using Euclid's algorithm

Highest Common Factor of 580,666,667 is 1

Step 1: Since 666 > 580, we apply the division lemma to 666 and 580, to get

666 = 580 x 1 + 86

Step 2: Since the reminder 580 ≠ 0, we apply division lemma to 86 and 580, to get

580 = 86 x 6 + 64

Step 3: We consider the new divisor 86 and the new remainder 64, and apply the division lemma to get

86 = 64 x 1 + 22

We consider the new divisor 64 and the new remainder 22,and apply the division lemma to get

64 = 22 x 2 + 20

We consider the new divisor 22 and the new remainder 20,and apply the division lemma to get

22 = 20 x 1 + 2

We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get

20 = 2 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 580 and 666 is 2

Notice that 2 = HCF(20,2) = HCF(22,20) = HCF(64,22) = HCF(86,64) = HCF(580,86) = HCF(666,580) .

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

Step 1: Since 667 > 2, we apply the division lemma to 667 and 2, to get

667 = 2 x 333 + 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 667 is 1

Notice that 1 = HCF(2,1) = HCF(667,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 580, 666, 667 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 580, 666, 667?

Answer: HCF of 580, 666, 667 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 580, 666, 667 using Euclid's Algorithm?

Answer: For arbitrary numbers 580, 666, 667 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.