Highest Common Factor of 8187, 6075 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 8187, 6075 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 8187, 6075 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 8187, 6075 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 8187, 6075 is 3.
HCF(8187, 6075) = 3
HCF of 8187, 6075 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8187, 6075 is 3.
Highest Common Factor of 8187,6075 is 3
Step 1: Since 8187 > 6075, we apply the division lemma to 8187 and 6075, to get
8187 = 6075 x 1 + 2112
Step 2: Since the reminder 6075 ≠ 0, we apply division lemma to 2112 and 6075, to get
6075 = 2112 x 2 + 1851
Step 3: We consider the new divisor 2112 and the new remainder 1851, and apply the division lemma to get
2112 = 1851 x 1 + 261
We consider the new divisor 1851 and the new remainder 261,and apply the division lemma to get
1851 = 261 x 7 + 24
We consider the new divisor 261 and the new remainder 24,and apply the division lemma to get
261 = 24 x 10 + 21
We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get
24 = 21 x 1 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 8187 and 6075 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(261,24) = HCF(1851,261) = HCF(2112,1851) = HCF(6075,2112) = HCF(8187,6075) .
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Frequently Asked Questions on HCF of 8187, 6075 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 8187, 6075?
Answer: HCF of 8187, 6075 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8187, 6075 using Euclid's Algorithm?
Answer: For arbitrary numbers 8187, 6075 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.