Highest Common Factor of 6765, 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 6765, 7814 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 6765, 7814 is 1 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 6765, 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 6765, 7814 is 1.
HCF(6765, 7814) = 1
HCF of 6765, 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 6765, 7814 is 1.
Highest Common Factor of 6765,7814 is 1
Step 1: Since 7814 > 6765, we apply the division lemma to 7814 and 6765, to get
7814 = 6765 x 1 + 1049
Step 2: Since the reminder 6765 ≠ 0, we apply division lemma to 1049 and 6765, to get
6765 = 1049 x 6 + 471
Step 3: We consider the new divisor 1049 and the new remainder 471, and apply the division lemma to get
1049 = 471 x 2 + 107
We consider the new divisor 471 and the new remainder 107,and apply the division lemma to get
471 = 107 x 4 + 43
We consider the new divisor 107 and the new remainder 43,and apply the division lemma to get
107 = 43 x 2 + 21
We consider the new divisor 43 and the new remainder 21,and apply the division lemma to get
43 = 21 x 2 + 1
We consider the new divisor 21 and the new remainder 1,and apply the division lemma to get
21 = 1 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6765 and 7814 is 1
Notice that 1 = HCF(21,1) = HCF(43,21) = HCF(107,43) = HCF(471,107) = HCF(1049,471) = HCF(6765,1049) = HCF(7814,6765) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 6765, 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 6765, 7814?
Answer: HCF of 6765, 7814 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6765, 7814 using Euclid's Algorithm?
Answer: For arbitrary numbers 6765, 7814 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
