Highest Common Factor of 643, 870, 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 643, 870, 829 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 643, 870, 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 643, 870, 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 643, 870, 829 is 1.

HCF(643, 870, 829) = 1

HCF of 643, 870, 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 643, 870, 829 is 1.

Highest Common Factor of 643,870,829 using Euclid's algorithm

Highest Common Factor of 643,870,829 is 1

Step 1: Since 870 > 643, we apply the division lemma to 870 and 643, to get

870 = 643 x 1 + 227

Step 2: Since the reminder 643 ≠ 0, we apply division lemma to 227 and 643, to get

643 = 227 x 2 + 189

Step 3: We consider the new divisor 227 and the new remainder 189, and apply the division lemma to get

227 = 189 x 1 + 38

We consider the new divisor 189 and the new remainder 38,and apply the division lemma to get

189 = 38 x 4 + 37

We consider the new divisor 38 and the new remainder 37,and apply the division lemma to get

38 = 37 x 1 + 1

We consider the new divisor 37 and the new remainder 1,and apply the division lemma to get

37 = 1 x 37 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 643 and 870 is 1

Notice that 1 = HCF(37,1) = HCF(38,37) = HCF(189,38) = HCF(227,189) = HCF(643,227) = HCF(870,643) .

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

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

829 = 1 x 829 + 0

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

Notice that 1 = HCF(829,1) .

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Frequently Asked Questions on HCF of 643, 870, 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 643, 870, 829?

Answer: HCF of 643, 870, 829 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 643, 870, 829 using Euclid's Algorithm?

Answer: For arbitrary numbers 643, 870, 829 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.