Highest Common Factor of 7660, 6784 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 7660, 6784 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 7660, 6784 is 4 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 7660, 6784 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 7660, 6784 is 4.
HCF(7660, 6784) = 4
HCF of 7660, 6784 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7660, 6784 is 4.
Highest Common Factor of 7660,6784 is 4
Step 1: Since 7660 > 6784, we apply the division lemma to 7660 and 6784, to get
7660 = 6784 x 1 + 876
Step 2: Since the reminder 6784 ≠ 0, we apply division lemma to 876 and 6784, to get
6784 = 876 x 7 + 652
Step 3: We consider the new divisor 876 and the new remainder 652, and apply the division lemma to get
876 = 652 x 1 + 224
We consider the new divisor 652 and the new remainder 224,and apply the division lemma to get
652 = 224 x 2 + 204
We consider the new divisor 224 and the new remainder 204,and apply the division lemma to get
224 = 204 x 1 + 20
We consider the new divisor 204 and the new remainder 20,and apply the division lemma to get
204 = 20 x 10 + 4
We consider the new divisor 20 and the new remainder 4,and apply the division lemma to get
20 = 4 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 7660 and 6784 is 4
Notice that 4 = HCF(20,4) = HCF(204,20) = HCF(224,204) = HCF(652,224) = HCF(876,652) = HCF(6784,876) = HCF(7660,6784) .
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Frequently Asked Questions on HCF of 7660, 6784 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 7660, 6784?
Answer: HCF of 7660, 6784 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7660, 6784 using Euclid's Algorithm?
Answer: For arbitrary numbers 7660, 6784 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.