Highest Common Factor of 562, 829 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 562, 829 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 562, 829 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 562, 829 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 562, 829 is 1.

HCF(562, 829) = 1

HCF of 562, 829 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 562, 829 is 1.

Highest Common Factor of 562,829 using Euclid's algorithm

Highest Common Factor of 562,829 is 1

Step 1: Since 829 > 562, we apply the division lemma to 829 and 562, to get

829 = 562 x 1 + 267

Step 2: Since the reminder 562 ≠ 0, we apply division lemma to 267 and 562, to get

562 = 267 x 2 + 28

Step 3: We consider the new divisor 267 and the new remainder 28, and apply the division lemma to get

267 = 28 x 9 + 15

We consider the new divisor 28 and the new remainder 15,and apply the division lemma to get

28 = 15 x 1 + 13

We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get

15 = 13 x 1 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 562 and 829 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(28,15) = HCF(267,28) = HCF(562,267) = HCF(829,562) .

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Frequently Asked Questions on HCF of 562, 829 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 562, 829?

Answer: HCF of 562, 829 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 562, 829 using Euclid's Algorithm?

Answer: For arbitrary numbers 562, 829 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.