Highest Common Factor of 2586, 2421, 16983 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 2586, 2421, 16983 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 2586, 2421, 16983 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 2586, 2421, 16983 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 2586, 2421, 16983 is 3.
HCF(2586, 2421, 16983) = 3
HCF of 2586, 2421, 16983 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2586, 2421, 16983 is 3.
Highest Common Factor of 2586,2421,16983 is 3
Step 1: Since 2586 > 2421, we apply the division lemma to 2586 and 2421, to get
2586 = 2421 x 1 + 165
Step 2: Since the reminder 2421 ≠ 0, we apply division lemma to 165 and 2421, to get
2421 = 165 x 14 + 111
Step 3: We consider the new divisor 165 and the new remainder 111, and apply the division lemma to get
165 = 111 x 1 + 54
We consider the new divisor 111 and the new remainder 54,and apply the division lemma to get
111 = 54 x 2 + 3
We consider the new divisor 54 and the new remainder 3,and apply the division lemma to get
54 = 3 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 2586 and 2421 is 3
Notice that 3 = HCF(54,3) = HCF(111,54) = HCF(165,111) = HCF(2421,165) = HCF(2586,2421) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 16983 > 3, we apply the division lemma to 16983 and 3, to get
16983 = 3 x 5661 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 16983 is 3
Notice that 3 = HCF(16983,3) .
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Frequently Asked Questions on HCF of 2586, 2421, 16983 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 2586, 2421, 16983?
Answer: HCF of 2586, 2421, 16983 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2586, 2421, 16983 using Euclid's Algorithm?
Answer: For arbitrary numbers 2586, 2421, 16983 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.