Highest Common Factor of 813, 516, 974 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 813, 516, 974 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 813, 516, 974 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 813, 516, 974 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 813, 516, 974 is 1.

HCF(813, 516, 974) = 1

HCF of 813, 516, 974 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 813, 516, 974 is 1.

Highest Common Factor of 813,516,974 using Euclid's algorithm

Highest Common Factor of 813,516,974 is 1

Step 1: Since 813 > 516, we apply the division lemma to 813 and 516, to get

813 = 516 x 1 + 297

Step 2: Since the reminder 516 ≠ 0, we apply division lemma to 297 and 516, to get

516 = 297 x 1 + 219

Step 3: We consider the new divisor 297 and the new remainder 219, and apply the division lemma to get

297 = 219 x 1 + 78

We consider the new divisor 219 and the new remainder 78,and apply the division lemma to get

219 = 78 x 2 + 63

We consider the new divisor 78 and the new remainder 63,and apply the division lemma to get

78 = 63 x 1 + 15

We consider the new divisor 63 and the new remainder 15,and apply the division lemma to get

63 = 15 x 4 + 3

We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get

15 = 3 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 813 and 516 is 3

Notice that 3 = HCF(15,3) = HCF(63,15) = HCF(78,63) = HCF(219,78) = HCF(297,219) = HCF(516,297) = HCF(813,516) .

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

Step 1: Since 974 > 3, we apply the division lemma to 974 and 3, to get

974 = 3 x 324 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 3 and 974 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(974,3) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 813, 516, 974 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 813, 516, 974?

Answer: HCF of 813, 516, 974 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 813, 516, 974 using Euclid's Algorithm?

Answer: For arbitrary numbers 813, 516, 974 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.