Highest Common Factor of 687, 1665 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, 1665 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 687, 1665 is 3 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, 1665 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, 1665 is 3.
HCF(687, 1665) = 3
HCF of 687, 1665 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, 1665 is 3.
Highest Common Factor of 687,1665 is 3
Step 1: Since 1665 > 687, we apply the division lemma to 1665 and 687, to get
1665 = 687 x 2 + 291
Step 2: Since the reminder 687 ≠ 0, we apply division lemma to 291 and 687, to get
687 = 291 x 2 + 105
Step 3: We consider the new divisor 291 and the new remainder 105, and apply the division lemma to get
291 = 105 x 2 + 81
We consider the new divisor 105 and the new remainder 81,and apply the division lemma to get
105 = 81 x 1 + 24
We consider the new divisor 81 and the new remainder 24,and apply the division lemma to get
81 = 24 x 3 + 9
We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get
24 = 9 x 2 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 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 1665 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(81,24) = HCF(105,81) = HCF(291,105) = HCF(687,291) = HCF(1665,687) .
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Frequently Asked Questions on HCF of 687, 1665 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, 1665?
Answer: HCF of 687, 1665 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 687, 1665 using Euclid's Algorithm?
Answer: For arbitrary numbers 687, 1665 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
