Highest Common Factor of 2097, 765 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 2097, 765 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 2097, 765 is 9 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 2097, 765 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 2097, 765 is 9.
HCF(2097, 765) = 9
HCF of 2097, 765 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2097, 765 is 9.
Highest Common Factor of 2097,765 is 9
Step 1: Since 2097 > 765, we apply the division lemma to 2097 and 765, to get
2097 = 765 x 2 + 567
Step 2: Since the reminder 765 ≠ 0, we apply division lemma to 567 and 765, to get
765 = 567 x 1 + 198
Step 3: We consider the new divisor 567 and the new remainder 198, and apply the division lemma to get
567 = 198 x 2 + 171
We consider the new divisor 198 and the new remainder 171,and apply the division lemma to get
198 = 171 x 1 + 27
We consider the new divisor 171 and the new remainder 27,and apply the division lemma to get
171 = 27 x 6 + 9
We consider the new divisor 27 and the new remainder 9,and apply the division lemma to get
27 = 9 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 2097 and 765 is 9
Notice that 9 = HCF(27,9) = HCF(171,27) = HCF(198,171) = HCF(567,198) = HCF(765,567) = HCF(2097,765) .
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Frequently Asked Questions on HCF of 2097, 765 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 2097, 765?
Answer: HCF of 2097, 765 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2097, 765 using Euclid's Algorithm?
Answer: For arbitrary numbers 2097, 765 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.