Highest Common Factor of 268, 2082, 8368 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 268, 2082, 8368 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 268, 2082, 8368 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 268, 2082, 8368 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 268, 2082, 8368 is 2.
HCF(268, 2082, 8368) = 2
HCF of 268, 2082, 8368 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 268, 2082, 8368 is 2.
Highest Common Factor of 268,2082,8368 is 2
Step 1: Since 2082 > 268, we apply the division lemma to 2082 and 268, to get
2082 = 268 x 7 + 206
Step 2: Since the reminder 268 ≠ 0, we apply division lemma to 206 and 268, to get
268 = 206 x 1 + 62
Step 3: We consider the new divisor 206 and the new remainder 62, and apply the division lemma to get
206 = 62 x 3 + 20
We consider the new divisor 62 and the new remainder 20,and apply the division lemma to get
62 = 20 x 3 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 268 and 2082 is 2
Notice that 2 = HCF(20,2) = HCF(62,20) = HCF(206,62) = HCF(268,206) = HCF(2082,268) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8368 > 2, we apply the division lemma to 8368 and 2, to get
8368 = 2 x 4184 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 8368 is 2
Notice that 2 = HCF(8368,2) .
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Frequently Asked Questions on HCF of 268, 2082, 8368 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 268, 2082, 8368?
Answer: HCF of 268, 2082, 8368 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 268, 2082, 8368 using Euclid's Algorithm?
Answer: For arbitrary numbers 268, 2082, 8368 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.