Highest Common Factor of 82, 316, 230 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 82, 316, 230 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 82, 316, 230 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 82, 316, 230 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 82, 316, 230 is 2.
HCF(82, 316, 230) = 2
HCF of 82, 316, 230 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 82, 316, 230 is 2.
Highest Common Factor of 82,316,230 is 2
Step 1: Since 316 > 82, we apply the division lemma to 316 and 82, to get
316 = 82 x 3 + 70
Step 2: Since the reminder 82 ≠ 0, we apply division lemma to 70 and 82, to get
82 = 70 x 1 + 12
Step 3: We consider the new divisor 70 and the new remainder 12, and apply the division lemma to get
70 = 12 x 5 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 82 and 316 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(70,12) = HCF(82,70) = HCF(316,82) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 230 > 2, we apply the division lemma to 230 and 2, to get
230 = 2 x 115 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 230 is 2
Notice that 2 = HCF(230,2) .
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Frequently Asked Questions on HCF of 82, 316, 230 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 82, 316, 230?
Answer: HCF of 82, 316, 230 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 82, 316, 230 using Euclid's Algorithm?
Answer: For arbitrary numbers 82, 316, 230 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.