Highest Common Factor of 867, 15843 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 867, 15843 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 867, 15843 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 867, 15843 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 867, 15843 is 3.
HCF(867, 15843) = 3
HCF of 867, 15843 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 867, 15843 is 3.
Highest Common Factor of 867,15843 is 3
Step 1: Since 15843 > 867, we apply the division lemma to 15843 and 867, to get
15843 = 867 x 18 + 237
Step 2: Since the reminder 867 ≠ 0, we apply division lemma to 237 and 867, to get
867 = 237 x 3 + 156
Step 3: We consider the new divisor 237 and the new remainder 156, and apply the division lemma to get
237 = 156 x 1 + 81
We consider the new divisor 156 and the new remainder 81,and apply the division lemma to get
156 = 81 x 1 + 75
We consider the new divisor 81 and the new remainder 75,and apply the division lemma to get
81 = 75 x 1 + 6
We consider the new divisor 75 and the new remainder 6,and apply the division lemma to get
75 = 6 x 12 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 867 and 15843 is 3
Notice that 3 = HCF(6,3) = HCF(75,6) = HCF(81,75) = HCF(156,81) = HCF(237,156) = HCF(867,237) = HCF(15843,867) .
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Frequently Asked Questions on HCF of 867, 15843 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 867, 15843?
Answer: HCF of 867, 15843 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 867, 15843 using Euclid's Algorithm?
Answer: For arbitrary numbers 867, 15843 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.