Highest Common Factor of 208, 579, 660 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 208, 579, 660 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 208, 579, 660 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 208, 579, 660 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 208, 579, 660 is 1.

HCF(208, 579, 660) = 1

HCF of 208, 579, 660 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 208, 579, 660 is 1.

Highest Common Factor of 208,579,660 using Euclid's algorithm

Highest Common Factor of 208,579,660 is 1

Step 1: Since 579 > 208, we apply the division lemma to 579 and 208, to get

579 = 208 x 2 + 163

Step 2: Since the reminder 208 ≠ 0, we apply division lemma to 163 and 208, to get

208 = 163 x 1 + 45

Step 3: We consider the new divisor 163 and the new remainder 45, and apply the division lemma to get

163 = 45 x 3 + 28

We consider the new divisor 45 and the new remainder 28,and apply the division lemma to get

45 = 28 x 1 + 17

We consider the new divisor 28 and the new remainder 17,and apply the division lemma to get

28 = 17 x 1 + 11

We consider the new divisor 17 and the new remainder 11,and apply the division lemma to get

17 = 11 x 1 + 6

We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get

11 = 6 x 1 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 208 and 579 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(17,11) = HCF(28,17) = HCF(45,28) = HCF(163,45) = HCF(208,163) = HCF(579,208) .

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

Step 1: Since 660 > 1, we apply the division lemma to 660 and 1, to get

660 = 1 x 660 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 660 is 1

Notice that 1 = HCF(660,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 208, 579, 660 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 208, 579, 660?

Answer: HCF of 208, 579, 660 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 208, 579, 660 using Euclid's Algorithm?

Answer: For arbitrary numbers 208, 579, 660 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.