Highest Common Factor of 342, 212, 582 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 342, 212, 582 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 342, 212, 582 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 342, 212, 582 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 342, 212, 582 is 2.
HCF(342, 212, 582) = 2
HCF of 342, 212, 582 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 342, 212, 582 is 2.
Highest Common Factor of 342,212,582 is 2
Step 1: Since 342 > 212, we apply the division lemma to 342 and 212, to get
342 = 212 x 1 + 130
Step 2: Since the reminder 212 ≠ 0, we apply division lemma to 130 and 212, to get
212 = 130 x 1 + 82
Step 3: We consider the new divisor 130 and the new remainder 82, and apply the division lemma to get
130 = 82 x 1 + 48
We consider the new divisor 82 and the new remainder 48,and apply the division lemma to get
82 = 48 x 1 + 34
We consider the new divisor 48 and the new remainder 34,and apply the division lemma to get
48 = 34 x 1 + 14
We consider the new divisor 34 and the new remainder 14,and apply the division lemma to get
34 = 14 x 2 + 6
We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get
14 = 6 x 2 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 342 and 212 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(34,14) = HCF(48,34) = HCF(82,48) = HCF(130,82) = HCF(212,130) = HCF(342,212) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 582 > 2, we apply the division lemma to 582 and 2, to get
582 = 2 x 291 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 582 is 2
Notice that 2 = HCF(582,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 342, 212, 582 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 342, 212, 582?
Answer: HCF of 342, 212, 582 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 342, 212, 582 using Euclid's Algorithm?
Answer: For arbitrary numbers 342, 212, 582 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.