Highest Common Factor of 978, 2686, 1037 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 978, 2686, 1037 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 978, 2686, 1037 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 978, 2686, 1037 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 978, 2686, 1037 is 1.

HCF(978, 2686, 1037) = 1

HCF of 978, 2686, 1037 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 978, 2686, 1037 is 1.

Highest Common Factor of 978,2686,1037 using Euclid's algorithm

Highest Common Factor of 978,2686,1037 is 1

Step 1: Since 2686 > 978, we apply the division lemma to 2686 and 978, to get

2686 = 978 x 2 + 730

Step 2: Since the reminder 978 ≠ 0, we apply division lemma to 730 and 978, to get

978 = 730 x 1 + 248

Step 3: We consider the new divisor 730 and the new remainder 248, and apply the division lemma to get

730 = 248 x 2 + 234

We consider the new divisor 248 and the new remainder 234,and apply the division lemma to get

248 = 234 x 1 + 14

We consider the new divisor 234 and the new remainder 14,and apply the division lemma to get

234 = 14 x 16 + 10

We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get

14 = 10 x 1 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 978 and 2686 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(234,14) = HCF(248,234) = HCF(730,248) = HCF(978,730) = HCF(2686,978) .

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

Step 1: Since 1037 > 2, we apply the division lemma to 1037 and 2, to get

1037 = 2 x 518 + 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 1037 is 1

Notice that 1 = HCF(2,1) = HCF(1037,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 978, 2686, 1037 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 978, 2686, 1037?

Answer: HCF of 978, 2686, 1037 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 978, 2686, 1037 using Euclid's Algorithm?

Answer: For arbitrary numbers 978, 2686, 1037 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.