Highest Common Factor of 812, 524, 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 812, 524, 822 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 812, 524, 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 812, 524, 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 812, 524, 822 is 2.

HCF(812, 524, 822) = 2

HCF of 812, 524, 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 812, 524, 822 is 2.

Highest Common Factor of 812,524,822 using Euclid's algorithm

Highest Common Factor of 812,524,822 is 2

Step 1: Since 812 > 524, we apply the division lemma to 812 and 524, to get

812 = 524 x 1 + 288

Step 2: Since the reminder 524 ≠ 0, we apply division lemma to 288 and 524, to get

524 = 288 x 1 + 236

Step 3: We consider the new divisor 288 and the new remainder 236, and apply the division lemma to get

288 = 236 x 1 + 52

We consider the new divisor 236 and the new remainder 52,and apply the division lemma to get

236 = 52 x 4 + 28

We consider the new divisor 52 and the new remainder 28,and apply the division lemma to get

52 = 28 x 1 + 24

We consider the new divisor 28 and the new remainder 24,and apply the division lemma to get

28 = 24 x 1 + 4

We consider the new divisor 24 and the new remainder 4,and apply the division lemma to get

24 = 4 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 812 and 524 is 4

Notice that 4 = HCF(24,4) = HCF(28,24) = HCF(52,28) = HCF(236,52) = HCF(288,236) = HCF(524,288) = HCF(812,524) .

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

Step 1: Since 822 > 4, we apply the division lemma to 822 and 4, to get

822 = 4 x 205 + 2

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 822 is 2

Notice that 2 = HCF(4,2) = HCF(822,4) .

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Frequently Asked Questions on HCF of 812, 524, 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 812, 524, 822?

Answer: HCF of 812, 524, 822 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 812, 524, 822 using Euclid's Algorithm?

Answer: For arbitrary numbers 812, 524, 822 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.