Highest Common Factor of 2016, 8923 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 2016, 8923 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2016, 8923 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 2016, 8923 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 2016, 8923 is 1.
HCF(2016, 8923) = 1
HCF of 2016, 8923 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2016, 8923 is 1.
Highest Common Factor of 2016,8923 is 1
Step 1: Since 8923 > 2016, we apply the division lemma to 8923 and 2016, to get
8923 = 2016 x 4 + 859
Step 2: Since the reminder 2016 ≠ 0, we apply division lemma to 859 and 2016, to get
2016 = 859 x 2 + 298
Step 3: We consider the new divisor 859 and the new remainder 298, and apply the division lemma to get
859 = 298 x 2 + 263
We consider the new divisor 298 and the new remainder 263,and apply the division lemma to get
298 = 263 x 1 + 35
We consider the new divisor 263 and the new remainder 35,and apply the division lemma to get
263 = 35 x 7 + 18
We consider the new divisor 35 and the new remainder 18,and apply the division lemma to get
35 = 18 x 1 + 17
We consider the new divisor 18 and the new remainder 17,and apply the division lemma to get
18 = 17 x 1 + 1
We consider the new divisor 17 and the new remainder 1,and apply the division lemma to get
17 = 1 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2016 and 8923 is 1
Notice that 1 = HCF(17,1) = HCF(18,17) = HCF(35,18) = HCF(263,35) = HCF(298,263) = HCF(859,298) = HCF(2016,859) = HCF(8923,2016) .
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Frequently Asked Questions on HCF of 2016, 8923 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 2016, 8923?
Answer: HCF of 2016, 8923 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2016, 8923 using Euclid's Algorithm?
Answer: For arbitrary numbers 2016, 8923 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.