Highest Common Factor of 501, 8213 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 501, 8213 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 501, 8213 is 1 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 501, 8213 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 501, 8213 is 1.
HCF(501, 8213) = 1
HCF of 501, 8213 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 501, 8213 is 1.
Highest Common Factor of 501,8213 is 1
Step 1: Since 8213 > 501, we apply the division lemma to 8213 and 501, to get
8213 = 501 x 16 + 197
Step 2: Since the reminder 501 ≠ 0, we apply division lemma to 197 and 501, to get
501 = 197 x 2 + 107
Step 3: We consider the new divisor 197 and the new remainder 107, and apply the division lemma to get
197 = 107 x 1 + 90
We consider the new divisor 107 and the new remainder 90,and apply the division lemma to get
107 = 90 x 1 + 17
We consider the new divisor 90 and the new remainder 17,and apply the division lemma to get
90 = 17 x 5 + 5
We consider the new divisor 17 and the new remainder 5,and apply the division lemma to get
17 = 5 x 3 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 501 and 8213 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17,5) = HCF(90,17) = HCF(107,90) = HCF(197,107) = HCF(501,197) = HCF(8213,501) .
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Frequently Asked Questions on HCF of 501, 8213 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 501, 8213?
Answer: HCF of 501, 8213 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 501, 8213 using Euclid's Algorithm?
Answer: For arbitrary numbers 501, 8213 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.