Highest Common Factor of 687, 5946, 2145 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, 5946, 2145 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 687, 5946, 2145 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, 5946, 2145 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, 5946, 2145 is 3.
HCF(687, 5946, 2145) = 3
HCF of 687, 5946, 2145 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, 5946, 2145 is 3.
Highest Common Factor of 687,5946,2145 is 3
Step 1: Since 5946 > 687, we apply the division lemma to 5946 and 687, to get
5946 = 687 x 8 + 450
Step 2: Since the reminder 687 ≠ 0, we apply division lemma to 450 and 687, to get
687 = 450 x 1 + 237
Step 3: We consider the new divisor 450 and the new remainder 237, and apply the division lemma to get
450 = 237 x 1 + 213
We consider the new divisor 237 and the new remainder 213,and apply the division lemma to get
237 = 213 x 1 + 24
We consider the new divisor 213 and the new remainder 24,and apply the division lemma to get
213 = 24 x 8 + 21
We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get
24 = 21 x 1 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 687 and 5946 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(213,24) = HCF(237,213) = HCF(450,237) = HCF(687,450) = HCF(5946,687) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2145 > 3, we apply the division lemma to 2145 and 3, to get
2145 = 3 x 715 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 2145 is 3
Notice that 3 = HCF(2145,3) .
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Frequently Asked Questions on HCF of 687, 5946, 2145 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, 5946, 2145?
Answer: HCF of 687, 5946, 2145 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 687, 5946, 2145 using Euclid's Algorithm?
Answer: For arbitrary numbers 687, 5946, 2145 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.