Highest Common Factor of 6374, 2748 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, 2748 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 6374, 2748 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, 2748 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, 2748 is 2.
HCF(6374, 2748) = 2
HCF of 6374, 2748 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, 2748 is 2.
Highest Common Factor of 6374,2748 is 2
Step 1: Since 6374 > 2748, we apply the division lemma to 6374 and 2748, to get
6374 = 2748 x 2 + 878
Step 2: Since the reminder 2748 ≠ 0, we apply division lemma to 878 and 2748, to get
2748 = 878 x 3 + 114
Step 3: We consider the new divisor 878 and the new remainder 114, and apply the division lemma to get
878 = 114 x 7 + 80
We consider the new divisor 114 and the new remainder 80,and apply the division lemma to get
114 = 80 x 1 + 34
We consider the new divisor 80 and the new remainder 34,and apply the division lemma to get
80 = 34 x 2 + 12
We consider the new divisor 34 and the new remainder 12,and apply the division lemma to get
34 = 12 x 2 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6374 and 2748 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(34,12) = HCF(80,34) = HCF(114,80) = HCF(878,114) = HCF(2748,878) = HCF(6374,2748) .
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Frequently Asked Questions on HCF of 6374, 2748 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, 2748?
Answer: HCF of 6374, 2748 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6374, 2748 using Euclid's Algorithm?
Answer: For arbitrary numbers 6374, 2748 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
