Highest Common Factor of 501, 638 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, 638 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 501, 638 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, 638 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, 638 is 1.
HCF(501, 638) = 1
HCF of 501, 638 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, 638 is 1.
Highest Common Factor of 501,638 is 1
Step 1: Since 638 > 501, we apply the division lemma to 638 and 501, to get
638 = 501 x 1 + 137
Step 2: Since the reminder 501 ≠ 0, we apply division lemma to 137 and 501, to get
501 = 137 x 3 + 90
Step 3: We consider the new divisor 137 and the new remainder 90, and apply the division lemma to get
137 = 90 x 1 + 47
We consider the new divisor 90 and the new remainder 47,and apply the division lemma to get
90 = 47 x 1 + 43
We consider the new divisor 47 and the new remainder 43,and apply the division lemma to get
47 = 43 x 1 + 4
We consider the new divisor 43 and the new remainder 4,and apply the division lemma to get
43 = 4 x 10 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 501 and 638 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(43,4) = HCF(47,43) = HCF(90,47) = HCF(137,90) = HCF(501,137) = HCF(638,501) .
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Frequently Asked Questions on HCF of 501, 638 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, 638?
Answer: HCF of 501, 638 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 501, 638 using Euclid's Algorithm?
Answer: For arbitrary numbers 501, 638 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.