Highest Common Factor of 643, 813, 853 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, 813, 853 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 643, 813, 853 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, 813, 853 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, 813, 853 is 1.

HCF(643, 813, 853) = 1

HCF of 643, 813, 853 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, 813, 853 is 1.

Highest Common Factor of 643,813,853 using Euclid's algorithm

Highest Common Factor of 643,813,853 is 1

Step 1: Since 813 > 643, we apply the division lemma to 813 and 643, to get

813 = 643 x 1 + 170

Step 2: Since the reminder 643 ≠ 0, we apply division lemma to 170 and 643, to get

643 = 170 x 3 + 133

Step 3: We consider the new divisor 170 and the new remainder 133, and apply the division lemma to get

170 = 133 x 1 + 37

We consider the new divisor 133 and the new remainder 37,and apply the division lemma to get

133 = 37 x 3 + 22

We consider the new divisor 37 and the new remainder 22,and apply the division lemma to get

37 = 22 x 1 + 15

We consider the new divisor 22 and the new remainder 15,and apply the division lemma to get

22 = 15 x 1 + 7

We consider the new divisor 15 and the new remainder 7,and apply the division lemma to get

15 = 7 x 2 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 643 and 813 is 1

Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(22,15) = HCF(37,22) = HCF(133,37) = HCF(170,133) = HCF(643,170) = HCF(813,643) .

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

Step 1: Since 853 > 1, we apply the division lemma to 853 and 1, to get

853 = 1 x 853 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 853 is 1

Notice that 1 = HCF(853,1) .

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Frequently Asked Questions on HCF of 643, 813, 853 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, 813, 853?

Answer: HCF of 643, 813, 853 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 643, 813, 853 using Euclid's Algorithm?

Answer: For arbitrary numbers 643, 813, 853 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.