Highest Common Factor of 714, 4866, 6405 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 714, 4866, 6405 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 714, 4866, 6405 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 714, 4866, 6405 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 714, 4866, 6405 is 3.
HCF(714, 4866, 6405) = 3
HCF of 714, 4866, 6405 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 714, 4866, 6405 is 3.
Highest Common Factor of 714,4866,6405 is 3
Step 1: Since 4866 > 714, we apply the division lemma to 4866 and 714, to get
4866 = 714 x 6 + 582
Step 2: Since the reminder 714 ≠ 0, we apply division lemma to 582 and 714, to get
714 = 582 x 1 + 132
Step 3: We consider the new divisor 582 and the new remainder 132, and apply the division lemma to get
582 = 132 x 4 + 54
We consider the new divisor 132 and the new remainder 54,and apply the division lemma to get
132 = 54 x 2 + 24
We consider the new divisor 54 and the new remainder 24,and apply the division lemma to get
54 = 24 x 2 + 6
We consider the new divisor 24 and the new remainder 6,and apply the division lemma to get
24 = 6 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 714 and 4866 is 6
Notice that 6 = HCF(24,6) = HCF(54,24) = HCF(132,54) = HCF(582,132) = HCF(714,582) = HCF(4866,714) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6405 > 6, we apply the division lemma to 6405 and 6, to get
6405 = 6 x 1067 + 3
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 3 and 6, 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 6 and 6405 is 3
Notice that 3 = HCF(6,3) = HCF(6405,6) .
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Frequently Asked Questions on HCF of 714, 4866, 6405 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 714, 4866, 6405?
Answer: HCF of 714, 4866, 6405 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 714, 4866, 6405 using Euclid's Algorithm?
Answer: For arbitrary numbers 714, 4866, 6405 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
