Highest Common Factor of 6888, 8667 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 6888, 8667 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 6888, 8667 is 3 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 6888, 8667 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 6888, 8667 is 3.
HCF(6888, 8667) = 3
HCF of 6888, 8667 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6888, 8667 is 3.
Highest Common Factor of 6888,8667 is 3
Step 1: Since 8667 > 6888, we apply the division lemma to 8667 and 6888, to get
8667 = 6888 x 1 + 1779
Step 2: Since the reminder 6888 ≠ 0, we apply division lemma to 1779 and 6888, to get
6888 = 1779 x 3 + 1551
Step 3: We consider the new divisor 1779 and the new remainder 1551, and apply the division lemma to get
1779 = 1551 x 1 + 228
We consider the new divisor 1551 and the new remainder 228,and apply the division lemma to get
1551 = 228 x 6 + 183
We consider the new divisor 228 and the new remainder 183,and apply the division lemma to get
228 = 183 x 1 + 45
We consider the new divisor 183 and the new remainder 45,and apply the division lemma to get
183 = 45 x 4 + 3
We consider the new divisor 45 and the new remainder 3,and apply the division lemma to get
45 = 3 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6888 and 8667 is 3
Notice that 3 = HCF(45,3) = HCF(183,45) = HCF(228,183) = HCF(1551,228) = HCF(1779,1551) = HCF(6888,1779) = HCF(8667,6888) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 6888, 8667 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 6888, 8667?
Answer: HCF of 6888, 8667 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6888, 8667 using Euclid's Algorithm?
Answer: For arbitrary numbers 6888, 8667 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.