Highest Common Factor of 502, 5727 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 502, 5727 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 502, 5727 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 502, 5727 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 502, 5727 is 1.
HCF(502, 5727) = 1
HCF of 502, 5727 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 502, 5727 is 1.
Highest Common Factor of 502,5727 is 1
Step 1: Since 5727 > 502, we apply the division lemma to 5727 and 502, to get
5727 = 502 x 11 + 205
Step 2: Since the reminder 502 ≠ 0, we apply division lemma to 205 and 502, to get
502 = 205 x 2 + 92
Step 3: We consider the new divisor 205 and the new remainder 92, and apply the division lemma to get
205 = 92 x 2 + 21
We consider the new divisor 92 and the new remainder 21,and apply the division lemma to get
92 = 21 x 4 + 8
We consider the new divisor 21 and the new remainder 8,and apply the division lemma to get
21 = 8 x 2 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 502 and 5727 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(92,21) = HCF(205,92) = HCF(502,205) = HCF(5727,502) .
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Frequently Asked Questions on HCF of 502, 5727 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 502, 5727?
Answer: HCF of 502, 5727 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 502, 5727 using Euclid's Algorithm?
Answer: For arbitrary numbers 502, 5727 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.