Highest Common Factor of 478, 2037 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 478, 2037 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 478, 2037 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 478, 2037 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 478, 2037 is 1.
HCF(478, 2037) = 1
HCF of 478, 2037 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 478, 2037 is 1.
Highest Common Factor of 478,2037 is 1
Step 1: Since 2037 > 478, we apply the division lemma to 2037 and 478, to get
2037 = 478 x 4 + 125
Step 2: Since the reminder 478 ≠ 0, we apply division lemma to 125 and 478, to get
478 = 125 x 3 + 103
Step 3: We consider the new divisor 125 and the new remainder 103, and apply the division lemma to get
125 = 103 x 1 + 22
We consider the new divisor 103 and the new remainder 22,and apply the division lemma to get
103 = 22 x 4 + 15
We consider the new divisor 22 and the new remainder 15,and apply the division lemma to get
22 = 15 x 1 + 7
We consider the new divisor 15 and the new remainder 7,and apply the division lemma to get
15 = 7 x 2 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 478 and 2037 is 1
Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(22,15) = HCF(103,22) = HCF(125,103) = HCF(478,125) = HCF(2037,478) .
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Frequently Asked Questions on HCF of 478, 2037 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 478, 2037?
Answer: HCF of 478, 2037 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 478, 2037 using Euclid's Algorithm?
Answer: For arbitrary numbers 478, 2037 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.