Highest Common Factor of 867, 567, 674 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 867, 567, 674 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 867, 567, 674 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 867, 567, 674 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 867, 567, 674 is 1.

HCF(867, 567, 674) = 1

HCF of 867, 567, 674 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 867, 567, 674 is 1.

Highest Common Factor of 867,567,674 using Euclid's algorithm

Highest Common Factor of 867,567,674 is 1

Step 1: Since 867 > 567, we apply the division lemma to 867 and 567, to get

867 = 567 x 1 + 300

Step 2: Since the reminder 567 ≠ 0, we apply division lemma to 300 and 567, to get

567 = 300 x 1 + 267

Step 3: We consider the new divisor 300 and the new remainder 267, and apply the division lemma to get

300 = 267 x 1 + 33

We consider the new divisor 267 and the new remainder 33,and apply the division lemma to get

267 = 33 x 8 + 3

We consider the new divisor 33 and the new remainder 3,and apply the division lemma to get

33 = 3 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 867 and 567 is 3

Notice that 3 = HCF(33,3) = HCF(267,33) = HCF(300,267) = HCF(567,300) = HCF(867,567) .

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

Step 1: Since 674 > 3, we apply the division lemma to 674 and 3, to get

674 = 3 x 224 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 674 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(674,3) .

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Frequently Asked Questions on HCF of 867, 567, 674 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 867, 567, 674?

Answer: HCF of 867, 567, 674 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 867, 567, 674 using Euclid's Algorithm?

Answer: For arbitrary numbers 867, 567, 674 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.