Highest Common Factor of 8916, 8218 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 8916, 8218 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8916, 8218 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 8916, 8218 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 8916, 8218 is 2.
HCF(8916, 8218) = 2
HCF of 8916, 8218 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8916, 8218 is 2.
Highest Common Factor of 8916,8218 is 2
Step 1: Since 8916 > 8218, we apply the division lemma to 8916 and 8218, to get
8916 = 8218 x 1 + 698
Step 2: Since the reminder 8218 ≠ 0, we apply division lemma to 698 and 8218, to get
8218 = 698 x 11 + 540
Step 3: We consider the new divisor 698 and the new remainder 540, and apply the division lemma to get
698 = 540 x 1 + 158
We consider the new divisor 540 and the new remainder 158,and apply the division lemma to get
540 = 158 x 3 + 66
We consider the new divisor 158 and the new remainder 66,and apply the division lemma to get
158 = 66 x 2 + 26
We consider the new divisor 66 and the new remainder 26,and apply the division lemma to get
66 = 26 x 2 + 14
We consider the new divisor 26 and the new remainder 14,and apply the division lemma to get
26 = 14 x 1 + 12
We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get
14 = 12 x 1 + 2
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 8916 and 8218 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(66,26) = HCF(158,66) = HCF(540,158) = HCF(698,540) = HCF(8218,698) = HCF(8916,8218) .
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Frequently Asked Questions on HCF of 8916, 8218 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 8916, 8218?
Answer: HCF of 8916, 8218 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8916, 8218 using Euclid's Algorithm?
Answer: For arbitrary numbers 8916, 8218 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
