Highest Common Factor of 84, 518, 586 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 84, 518, 586 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 84, 518, 586 is 2 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 84, 518, 586 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 84, 518, 586 is 2.
HCF(84, 518, 586) = 2
HCF of 84, 518, 586 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 84, 518, 586 is 2.
Highest Common Factor of 84,518,586 is 2
Step 1: Since 518 > 84, we apply the division lemma to 518 and 84, to get
518 = 84 x 6 + 14
Step 2: Since the reminder 84 ≠ 0, we apply division lemma to 14 and 84, to get
84 = 14 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 84 and 518 is 14
Notice that 14 = HCF(84,14) = HCF(518,84) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 586 > 14, we apply the division lemma to 586 and 14, to get
586 = 14 x 41 + 12
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 12 and 14, to get
14 = 12 x 1 + 2
Step 3: We consider the new divisor 12 and the new remainder 2, and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 14 and 586 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(586,14) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 84, 518, 586 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 84, 518, 586?
Answer: HCF of 84, 518, 586 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 84, 518, 586 using Euclid's Algorithm?
Answer: For arbitrary numbers 84, 518, 586 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.