Highest Common Factor of 561, 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 561, 765 i.e. 51 the largest integer that leaves a remainder zero for all numbers.
HCF of 561, 765 is 51 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 561, 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 561, 765 is 51.
HCF(561, 765) = 51
HCF of 561, 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 561, 765 is 51.
Highest Common Factor of 561,765 is 51
Step 1: Since 765 > 561, we apply the division lemma to 765 and 561, to get
765 = 561 x 1 + 204
Step 2: Since the reminder 561 ≠ 0, we apply division lemma to 204 and 561, to get
561 = 204 x 2 + 153
Step 3: We consider the new divisor 204 and the new remainder 153, and apply the division lemma to get
204 = 153 x 1 + 51
We consider the new divisor 153 and the new remainder 51, and apply the division lemma to get
153 = 51 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 51, the HCF of 561 and 765 is 51
Notice that 51 = HCF(153,51) = HCF(204,153) = HCF(561,204) = HCF(765,561) .
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Frequently Asked Questions on HCF of 561, 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 561, 765?
Answer: HCF of 561, 765 is 51 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 561, 765 using Euclid's Algorithm?
Answer: For arbitrary numbers 561, 765 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.