Highest Common Factor of 2373, 538 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 2373, 538 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2373, 538 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 2373, 538 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 2373, 538 is 1.
HCF(2373, 538) = 1
HCF of 2373, 538 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2373, 538 is 1.
Highest Common Factor of 2373,538 is 1
Step 1: Since 2373 > 538, we apply the division lemma to 2373 and 538, to get
2373 = 538 x 4 + 221
Step 2: Since the reminder 538 ≠ 0, we apply division lemma to 221 and 538, to get
538 = 221 x 2 + 96
Step 3: We consider the new divisor 221 and the new remainder 96, and apply the division lemma to get
221 = 96 x 2 + 29
We consider the new divisor 96 and the new remainder 29,and apply the division lemma to get
96 = 29 x 3 + 9
We consider the new divisor 29 and the new remainder 9,and apply the division lemma to get
29 = 9 x 3 + 2
We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get
9 = 2 x 4 + 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 2373 and 538 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(29,9) = HCF(96,29) = HCF(221,96) = HCF(538,221) = HCF(2373,538) .
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Frequently Asked Questions on HCF of 2373, 538 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 2373, 538?
Answer: HCF of 2373, 538 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2373, 538 using Euclid's Algorithm?
Answer: For arbitrary numbers 2373, 538 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.