Highest Common Factor of 974, 708, 822 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 974, 708, 822 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 974, 708, 822 is 2 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 974, 708, 822 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 974, 708, 822 is 2.

HCF(974, 708, 822) = 2

HCF of 974, 708, 822 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 974, 708, 822 is 2.

Highest Common Factor of 974,708,822 using Euclid's algorithm

Highest Common Factor of 974,708,822 is 2

Step 1: Since 974 > 708, we apply the division lemma to 974 and 708, to get

974 = 708 x 1 + 266

Step 2: Since the reminder 708 ≠ 0, we apply division lemma to 266 and 708, to get

708 = 266 x 2 + 176

Step 3: We consider the new divisor 266 and the new remainder 176, and apply the division lemma to get

266 = 176 x 1 + 90

We consider the new divisor 176 and the new remainder 90,and apply the division lemma to get

176 = 90 x 1 + 86

We consider the new divisor 90 and the new remainder 86,and apply the division lemma to get

90 = 86 x 1 + 4

We consider the new divisor 86 and the new remainder 4,and apply the division lemma to get

86 = 4 x 21 + 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 974 and 708 is 2

Notice that 2 = HCF(4,2) = HCF(86,4) = HCF(90,86) = HCF(176,90) = HCF(266,176) = HCF(708,266) = HCF(974,708) .

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

Step 1: Since 822 > 2, we apply the division lemma to 822 and 2, to get

822 = 2 x 411 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 822 is 2

Notice that 2 = HCF(822,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 974, 708, 822 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 974, 708, 822?

Answer: HCF of 974, 708, 822 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 974, 708, 822 using Euclid's Algorithm?

Answer: For arbitrary numbers 974, 708, 822 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.