Highest Common Factor of 2373, 9135 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, 9135 i.e. 21 the largest integer that leaves a remainder zero for all numbers.
HCF of 2373, 9135 is 21 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, 9135 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, 9135 is 21.
HCF(2373, 9135) = 21
HCF of 2373, 9135 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, 9135 is 21.
Highest Common Factor of 2373,9135 is 21
Step 1: Since 9135 > 2373, we apply the division lemma to 9135 and 2373, to get
9135 = 2373 x 3 + 2016
Step 2: Since the reminder 2373 ≠ 0, we apply division lemma to 2016 and 2373, to get
2373 = 2016 x 1 + 357
Step 3: We consider the new divisor 2016 and the new remainder 357, and apply the division lemma to get
2016 = 357 x 5 + 231
We consider the new divisor 357 and the new remainder 231,and apply the division lemma to get
357 = 231 x 1 + 126
We consider the new divisor 231 and the new remainder 126,and apply the division lemma to get
231 = 126 x 1 + 105
We consider the new divisor 126 and the new remainder 105,and apply the division lemma to get
126 = 105 x 1 + 21
We consider the new divisor 105 and the new remainder 21,and apply the division lemma to get
105 = 21 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 2373 and 9135 is 21
Notice that 21 = HCF(105,21) = HCF(126,105) = HCF(231,126) = HCF(357,231) = HCF(2016,357) = HCF(2373,2016) = HCF(9135,2373) .
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Frequently Asked Questions on HCF of 2373, 9135 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, 9135?
Answer: HCF of 2373, 9135 is 21 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2373, 9135 using Euclid's Algorithm?
Answer: For arbitrary numbers 2373, 9135 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.