Highest Common Factor of 522, 983, 823 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 522, 983, 823 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 522, 983, 823 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 522, 983, 823 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 522, 983, 823 is 1.

HCF(522, 983, 823) = 1

HCF of 522, 983, 823 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 522, 983, 823 is 1.

Highest Common Factor of 522,983,823 using Euclid's algorithm

Highest Common Factor of 522,983,823 is 1

Step 1: Since 983 > 522, we apply the division lemma to 983 and 522, to get

983 = 522 x 1 + 461

Step 2: Since the reminder 522 ≠ 0, we apply division lemma to 461 and 522, to get

522 = 461 x 1 + 61

Step 3: We consider the new divisor 461 and the new remainder 61, and apply the division lemma to get

461 = 61 x 7 + 34

We consider the new divisor 61 and the new remainder 34,and apply the division lemma to get

61 = 34 x 1 + 27

We consider the new divisor 34 and the new remainder 27,and apply the division lemma to get

34 = 27 x 1 + 7

We consider the new divisor 27 and the new remainder 7,and apply the division lemma to get

27 = 7 x 3 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 522 and 983 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(27,7) = HCF(34,27) = HCF(61,34) = HCF(461,61) = HCF(522,461) = HCF(983,522) .

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

Step 1: Since 823 > 1, we apply the division lemma to 823 and 1, to get

823 = 1 x 823 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 823 is 1

Notice that 1 = HCF(823,1) .

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Frequently Asked Questions on HCF of 522, 983, 823 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 522, 983, 823?

Answer: HCF of 522, 983, 823 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 522, 983, 823 using Euclid's Algorithm?

Answer: For arbitrary numbers 522, 983, 823 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.