Highest Common Factor of 6374, 7856 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 6374, 7856 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 6374, 7856 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 6374, 7856 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 6374, 7856 is 2.
HCF(6374, 7856) = 2
HCF of 6374, 7856 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6374, 7856 is 2.
Highest Common Factor of 6374,7856 is 2
Step 1: Since 7856 > 6374, we apply the division lemma to 7856 and 6374, to get
7856 = 6374 x 1 + 1482
Step 2: Since the reminder 6374 ≠ 0, we apply division lemma to 1482 and 6374, to get
6374 = 1482 x 4 + 446
Step 3: We consider the new divisor 1482 and the new remainder 446, and apply the division lemma to get
1482 = 446 x 3 + 144
We consider the new divisor 446 and the new remainder 144,and apply the division lemma to get
446 = 144 x 3 + 14
We consider the new divisor 144 and the new remainder 14,and apply the division lemma to get
144 = 14 x 10 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6374 and 7856 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(144,14) = HCF(446,144) = HCF(1482,446) = HCF(6374,1482) = HCF(7856,6374) .
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Frequently Asked Questions on HCF of 6374, 7856 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 6374, 7856?
Answer: HCF of 6374, 7856 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6374, 7856 using Euclid's Algorithm?
Answer: For arbitrary numbers 6374, 7856 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.