Highest Common Factor of 864, 623 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 864, 623 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 864, 623 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 864, 623 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 864, 623 is 1.

HCF(864, 623) = 1

HCF of 864, 623 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 864, 623 is 1.

Highest Common Factor of 864,623 using Euclid's algorithm

Highest Common Factor of 864,623 is 1

Step 1: Since 864 > 623, we apply the division lemma to 864 and 623, to get

864 = 623 x 1 + 241

Step 2: Since the reminder 623 ≠ 0, we apply division lemma to 241 and 623, to get

623 = 241 x 2 + 141

Step 3: We consider the new divisor 241 and the new remainder 141, and apply the division lemma to get

241 = 141 x 1 + 100

We consider the new divisor 141 and the new remainder 100,and apply the division lemma to get

141 = 100 x 1 + 41

We consider the new divisor 100 and the new remainder 41,and apply the division lemma to get

100 = 41 x 2 + 18

We consider the new divisor 41 and the new remainder 18,and apply the division lemma to get

41 = 18 x 2 + 5

We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get

18 = 5 x 3 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 864 and 623 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(41,18) = HCF(100,41) = HCF(141,100) = HCF(241,141) = HCF(623,241) = HCF(864,623) .

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Frequently Asked Questions on HCF of 864, 623 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 864, 623?

Answer: HCF of 864, 623 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 864, 623 using Euclid's Algorithm?

Answer: For arbitrary numbers 864, 623 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.