Highest Common Factor of 8518, 3178 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 8518, 3178 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8518, 3178 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 8518, 3178 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 8518, 3178 is 2.
HCF(8518, 3178) = 2
HCF of 8518, 3178 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8518, 3178 is 2.
Highest Common Factor of 8518,3178 is 2
Step 1: Since 8518 > 3178, we apply the division lemma to 8518 and 3178, to get
8518 = 3178 x 2 + 2162
Step 2: Since the reminder 3178 ≠ 0, we apply division lemma to 2162 and 3178, to get
3178 = 2162 x 1 + 1016
Step 3: We consider the new divisor 2162 and the new remainder 1016, and apply the division lemma to get
2162 = 1016 x 2 + 130
We consider the new divisor 1016 and the new remainder 130,and apply the division lemma to get
1016 = 130 x 7 + 106
We consider the new divisor 130 and the new remainder 106,and apply the division lemma to get
130 = 106 x 1 + 24
We consider the new divisor 106 and the new remainder 24,and apply the division lemma to get
106 = 24 x 4 + 10
We consider the new divisor 24 and the new remainder 10,and apply the division lemma to get
24 = 10 x 2 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8518 and 3178 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(24,10) = HCF(106,24) = HCF(130,106) = HCF(1016,130) = HCF(2162,1016) = HCF(3178,2162) = HCF(8518,3178) .
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Frequently Asked Questions on HCF of 8518, 3178 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 8518, 3178?
Answer: HCF of 8518, 3178 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8518, 3178 using Euclid's Algorithm?
Answer: For arbitrary numbers 8518, 3178 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.