Highest Common Factor of 564, 2605 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 564, 2605 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 564, 2605 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 564, 2605 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 564, 2605 is 1.
HCF(564, 2605) = 1
HCF of 564, 2605 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 564, 2605 is 1.
Highest Common Factor of 564,2605 is 1
Step 1: Since 2605 > 564, we apply the division lemma to 2605 and 564, to get
2605 = 564 x 4 + 349
Step 2: Since the reminder 564 ≠ 0, we apply division lemma to 349 and 564, to get
564 = 349 x 1 + 215
Step 3: We consider the new divisor 349 and the new remainder 215, and apply the division lemma to get
349 = 215 x 1 + 134
We consider the new divisor 215 and the new remainder 134,and apply the division lemma to get
215 = 134 x 1 + 81
We consider the new divisor 134 and the new remainder 81,and apply the division lemma to get
134 = 81 x 1 + 53
We consider the new divisor 81 and the new remainder 53,and apply the division lemma to get
81 = 53 x 1 + 28
We consider the new divisor 53 and the new remainder 28,and apply the division lemma to get
53 = 28 x 1 + 25
We consider the new divisor 28 and the new remainder 25,and apply the division lemma to get
28 = 25 x 1 + 3
We consider the new divisor 25 and the new remainder 3,and apply the division lemma to get
25 = 3 x 8 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 564 and 2605 is 1
Notice that 1 = HCF(3,1) = HCF(25,3) = HCF(28,25) = HCF(53,28) = HCF(81,53) = HCF(134,81) = HCF(215,134) = HCF(349,215) = HCF(564,349) = HCF(2605,564) .
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Frequently Asked Questions on HCF of 564, 2605 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 564, 2605?
Answer: HCF of 564, 2605 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 564, 2605 using Euclid's Algorithm?
Answer: For arbitrary numbers 564, 2605 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.