Highest Common Factor of 687, 759, 868 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 687, 759, 868 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 687, 759, 868 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 687, 759, 868 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 687, 759, 868 is 1.
HCF(687, 759, 868) = 1
HCF of 687, 759, 868 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 687, 759, 868 is 1.
Highest Common Factor of 687,759,868 is 1
Step 1: Since 759 > 687, we apply the division lemma to 759 and 687, to get
759 = 687 x 1 + 72
Step 2: Since the reminder 687 ≠ 0, we apply division lemma to 72 and 687, to get
687 = 72 x 9 + 39
Step 3: We consider the new divisor 72 and the new remainder 39, and apply the division lemma to get
72 = 39 x 1 + 33
We consider the new divisor 39 and the new remainder 33,and apply the division lemma to get
39 = 33 x 1 + 6
We consider the new divisor 33 and the new remainder 6,and apply the division lemma to get
33 = 6 x 5 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 687 and 759 is 3
Notice that 3 = HCF(6,3) = HCF(33,6) = HCF(39,33) = HCF(72,39) = HCF(687,72) = HCF(759,687) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 868 > 3, we apply the division lemma to 868 and 3, to get
868 = 3 x 289 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 868 is 1
Notice that 1 = HCF(3,1) = HCF(868,3) .
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Frequently Asked Questions on HCF of 687, 759, 868 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 687, 759, 868?
Answer: HCF of 687, 759, 868 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 687, 759, 868 using Euclid's Algorithm?
Answer: For arbitrary numbers 687, 759, 868 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
