Highest Common Factor of 821, 2244, 7823 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 821, 2244, 7823 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 821, 2244, 7823 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 821, 2244, 7823 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 821, 2244, 7823 is 1.

HCF(821, 2244, 7823) = 1

HCF of 821, 2244, 7823 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 821, 2244, 7823 is 1.

Highest Common Factor of 821,2244,7823 using Euclid's algorithm

Highest Common Factor of 821,2244,7823 is 1

Step 1: Since 2244 > 821, we apply the division lemma to 2244 and 821, to get

2244 = 821 x 2 + 602

Step 2: Since the reminder 821 ≠ 0, we apply division lemma to 602 and 821, to get

821 = 602 x 1 + 219

Step 3: We consider the new divisor 602 and the new remainder 219, and apply the division lemma to get

602 = 219 x 2 + 164

We consider the new divisor 219 and the new remainder 164,and apply the division lemma to get

219 = 164 x 1 + 55

We consider the new divisor 164 and the new remainder 55,and apply the division lemma to get

164 = 55 x 2 + 54

We consider the new divisor 55 and the new remainder 54,and apply the division lemma to get

55 = 54 x 1 + 1

We consider the new divisor 54 and the new remainder 1,and apply the division lemma to get

54 = 1 x 54 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 821 and 2244 is 1

Notice that 1 = HCF(54,1) = HCF(55,54) = HCF(164,55) = HCF(219,164) = HCF(602,219) = HCF(821,602) = HCF(2244,821) .

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

Step 1: Since 7823 > 1, we apply the division lemma to 7823 and 1, to get

7823 = 1 x 7823 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 7823 is 1

Notice that 1 = HCF(7823,1) .

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Frequently Asked Questions on HCF of 821, 2244, 7823 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 821, 2244, 7823?

Answer: HCF of 821, 2244, 7823 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 821, 2244, 7823 using Euclid's Algorithm?

Answer: For arbitrary numbers 821, 2244, 7823 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.