Highest Common Factor of 687, 5662 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, 5662 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 687, 5662 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, 5662 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, 5662 is 1.
HCF(687, 5662) = 1
HCF of 687, 5662 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, 5662 is 1.
Highest Common Factor of 687,5662 is 1
Step 1: Since 5662 > 687, we apply the division lemma to 5662 and 687, to get
5662 = 687 x 8 + 166
Step 2: Since the reminder 687 ≠ 0, we apply division lemma to 166 and 687, to get
687 = 166 x 4 + 23
Step 3: We consider the new divisor 166 and the new remainder 23, and apply the division lemma to get
166 = 23 x 7 + 5
We consider the new divisor 23 and the new remainder 5,and apply the division lemma to get
23 = 5 x 4 + 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 687 and 5662 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(23,5) = HCF(166,23) = HCF(687,166) = HCF(5662,687) .
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Frequently Asked Questions on HCF of 687, 5662 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, 5662?
Answer: HCF of 687, 5662 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 687, 5662 using Euclid's Algorithm?
Answer: For arbitrary numbers 687, 5662 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.