Highest Common Factor of 6408, 7814 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 6408, 7814 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 6408, 7814 is 2 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 6408, 7814 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 6408, 7814 is 2.
HCF(6408, 7814) = 2
HCF of 6408, 7814 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6408, 7814 is 2.
Highest Common Factor of 6408,7814 is 2
Step 1: Since 7814 > 6408, we apply the division lemma to 7814 and 6408, to get
7814 = 6408 x 1 + 1406
Step 2: Since the reminder 6408 ≠ 0, we apply division lemma to 1406 and 6408, to get
6408 = 1406 x 4 + 784
Step 3: We consider the new divisor 1406 and the new remainder 784, and apply the division lemma to get
1406 = 784 x 1 + 622
We consider the new divisor 784 and the new remainder 622,and apply the division lemma to get
784 = 622 x 1 + 162
We consider the new divisor 622 and the new remainder 162,and apply the division lemma to get
622 = 162 x 3 + 136
We consider the new divisor 162 and the new remainder 136,and apply the division lemma to get
162 = 136 x 1 + 26
We consider the new divisor 136 and the new remainder 26,and apply the division lemma to get
136 = 26 x 5 + 6
We consider the new divisor 26 and the new remainder 6,and apply the division lemma to get
26 = 6 x 4 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6408 and 7814 is 2
Notice that 2 = HCF(6,2) = HCF(26,6) = HCF(136,26) = HCF(162,136) = HCF(622,162) = HCF(784,622) = HCF(1406,784) = HCF(6408,1406) = HCF(7814,6408) .
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Frequently Asked Questions on HCF of 6408, 7814 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 6408, 7814?
Answer: HCF of 6408, 7814 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6408, 7814 using Euclid's Algorithm?
Answer: For arbitrary numbers 6408, 7814 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.