Highest Common Factor of 689, 702, 867 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 689, 702, 867 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 689, 702, 867 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 689, 702, 867 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 689, 702, 867 is 1.

HCF(689, 702, 867) = 1

HCF of 689, 702, 867 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 689, 702, 867 is 1.

Highest Common Factor of 689,702,867 using Euclid's algorithm

Highest Common Factor of 689,702,867 is 1

Step 1: Since 702 > 689, we apply the division lemma to 702 and 689, to get

702 = 689 x 1 + 13

Step 2: Since the reminder 689 ≠ 0, we apply division lemma to 13 and 689, to get

689 = 13 x 53 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 689 and 702 is 13

Notice that 13 = HCF(689,13) = HCF(702,689) .

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

Step 1: Since 867 > 13, we apply the division lemma to 867 and 13, to get

867 = 13 x 66 + 9

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 9 and 13, to get

13 = 9 x 1 + 4

Step 3: We consider the new divisor 9 and the new remainder 4, and apply the division lemma to get

9 = 4 x 2 + 1

We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 13 and 867 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(867,13) .

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Frequently Asked Questions on HCF of 689, 702, 867 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 689, 702, 867?

Answer: HCF of 689, 702, 867 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 689, 702, 867 using Euclid's Algorithm?

Answer: For arbitrary numbers 689, 702, 867 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.