Highest Common Factor of 6531, 7314 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 6531, 7314 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 6531, 7314 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 6531, 7314 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 6531, 7314 is 3.
HCF(6531, 7314) = 3
HCF of 6531, 7314 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6531, 7314 is 3.
Highest Common Factor of 6531,7314 is 3
Step 1: Since 7314 > 6531, we apply the division lemma to 7314 and 6531, to get
7314 = 6531 x 1 + 783
Step 2: Since the reminder 6531 ≠ 0, we apply division lemma to 783 and 6531, to get
6531 = 783 x 8 + 267
Step 3: We consider the new divisor 783 and the new remainder 267, and apply the division lemma to get
783 = 267 x 2 + 249
We consider the new divisor 267 and the new remainder 249,and apply the division lemma to get
267 = 249 x 1 + 18
We consider the new divisor 249 and the new remainder 18,and apply the division lemma to get
249 = 18 x 13 + 15
We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6531 and 7314 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(249,18) = HCF(267,249) = HCF(783,267) = HCF(6531,783) = HCF(7314,6531) .
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Frequently Asked Questions on HCF of 6531, 7314 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 6531, 7314?
Answer: HCF of 6531, 7314 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6531, 7314 using Euclid's Algorithm?
Answer: For arbitrary numbers 6531, 7314 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.