Highest Common Factor of 660, 886, 291 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 660, 886, 291 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 660, 886, 291 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 660, 886, 291 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 660, 886, 291 is 1.

HCF(660, 886, 291) = 1

HCF of 660, 886, 291 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 660, 886, 291 is 1.

Highest Common Factor of 660,886,291 using Euclid's algorithm

Highest Common Factor of 660,886,291 is 1

Step 1: Since 886 > 660, we apply the division lemma to 886 and 660, to get

886 = 660 x 1 + 226

Step 2: Since the reminder 660 ≠ 0, we apply division lemma to 226 and 660, to get

660 = 226 x 2 + 208

Step 3: We consider the new divisor 226 and the new remainder 208, and apply the division lemma to get

226 = 208 x 1 + 18

We consider the new divisor 208 and the new remainder 18,and apply the division lemma to get

208 = 18 x 11 + 10

We consider the new divisor 18 and the new remainder 10,and apply the division lemma to get

18 = 10 x 1 + 8

We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get

10 = 8 x 1 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 660 and 886 is 2

Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(208,18) = HCF(226,208) = HCF(660,226) = HCF(886,660) .

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

Step 1: Since 291 > 2, we apply the division lemma to 291 and 2, to get

291 = 2 x 145 + 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 291 is 1

Notice that 1 = HCF(2,1) = HCF(291,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 660, 886, 291 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 660, 886, 291?

Answer: HCF of 660, 886, 291 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 660, 886, 291 using Euclid's Algorithm?

Answer: For arbitrary numbers 660, 886, 291 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.