Highest Common Factor of 2259, 9645 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 2259, 9645 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 2259, 9645 is 3 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 2259, 9645 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 2259, 9645 is 3.
HCF(2259, 9645) = 3
HCF of 2259, 9645 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2259, 9645 is 3.
Highest Common Factor of 2259,9645 is 3
Step 1: Since 9645 > 2259, we apply the division lemma to 9645 and 2259, to get
9645 = 2259 x 4 + 609
Step 2: Since the reminder 2259 ≠ 0, we apply division lemma to 609 and 2259, to get
2259 = 609 x 3 + 432
Step 3: We consider the new divisor 609 and the new remainder 432, and apply the division lemma to get
609 = 432 x 1 + 177
We consider the new divisor 432 and the new remainder 177,and apply the division lemma to get
432 = 177 x 2 + 78
We consider the new divisor 177 and the new remainder 78,and apply the division lemma to get
177 = 78 x 2 + 21
We consider the new divisor 78 and the new remainder 21,and apply the division lemma to get
78 = 21 x 3 + 15
We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get
21 = 15 x 1 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 2259 and 9645 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(78,21) = HCF(177,78) = HCF(432,177) = HCF(609,432) = HCF(2259,609) = HCF(9645,2259) .
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Frequently Asked Questions on HCF of 2259, 9645 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 2259, 9645?
Answer: HCF of 2259, 9645 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2259, 9645 using Euclid's Algorithm?
Answer: For arbitrary numbers 2259, 9645 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.