Highest Common Factor of 564, 2084 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, 2084 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 564, 2084 is 4 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, 2084 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, 2084 is 4.
HCF(564, 2084) = 4
HCF of 564, 2084 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, 2084 is 4.
Highest Common Factor of 564,2084 is 4
Step 1: Since 2084 > 564, we apply the division lemma to 2084 and 564, to get
2084 = 564 x 3 + 392
Step 2: Since the reminder 564 ≠ 0, we apply division lemma to 392 and 564, to get
564 = 392 x 1 + 172
Step 3: We consider the new divisor 392 and the new remainder 172, and apply the division lemma to get
392 = 172 x 2 + 48
We consider the new divisor 172 and the new remainder 48,and apply the division lemma to get
172 = 48 x 3 + 28
We consider the new divisor 48 and the new remainder 28,and apply the division lemma to get
48 = 28 x 1 + 20
We consider the new divisor 28 and the new remainder 20,and apply the division lemma to get
28 = 20 x 1 + 8
We consider the new divisor 20 and the new remainder 8,and apply the division lemma to get
20 = 8 x 2 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 564 and 2084 is 4
Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(28,20) = HCF(48,28) = HCF(172,48) = HCF(392,172) = HCF(564,392) = HCF(2084,564) .
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Frequently Asked Questions on HCF of 564, 2084 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, 2084?
Answer: HCF of 564, 2084 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 564, 2084 using Euclid's Algorithm?
Answer: For arbitrary numbers 564, 2084 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.