Highest Common Factor of 823, 5222, 7154 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 823, 5222, 7154 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 823, 5222, 7154 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 823, 5222, 7154 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 823, 5222, 7154 is 1.

HCF(823, 5222, 7154) = 1

HCF of 823, 5222, 7154 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 823, 5222, 7154 is 1.

Highest Common Factor of 823,5222,7154 using Euclid's algorithm

Highest Common Factor of 823,5222,7154 is 1

Step 1: Since 5222 > 823, we apply the division lemma to 5222 and 823, to get

5222 = 823 x 6 + 284

Step 2: Since the reminder 823 ≠ 0, we apply division lemma to 284 and 823, to get

823 = 284 x 2 + 255

Step 3: We consider the new divisor 284 and the new remainder 255, and apply the division lemma to get

284 = 255 x 1 + 29

We consider the new divisor 255 and the new remainder 29,and apply the division lemma to get

255 = 29 x 8 + 23

We consider the new divisor 29 and the new remainder 23,and apply the division lemma to get

29 = 23 x 1 + 6

We consider the new divisor 23 and the new remainder 6,and apply the division lemma to get

23 = 6 x 3 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 823 and 5222 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(23,6) = HCF(29,23) = HCF(255,29) = HCF(284,255) = HCF(823,284) = HCF(5222,823) .

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

Step 1: Since 7154 > 1, we apply the division lemma to 7154 and 1, to get

7154 = 1 x 7154 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 7154 is 1

Notice that 1 = HCF(7154,1) .

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Frequently Asked Questions on HCF of 823, 5222, 7154 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 823, 5222, 7154?

Answer: HCF of 823, 5222, 7154 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 823, 5222, 7154 using Euclid's Algorithm?

Answer: For arbitrary numbers 823, 5222, 7154 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.