Highest Common Factor of 2006, 8588, 25692 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 2006, 8588, 25692 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2006, 8588, 25692 is 2 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 2006, 8588, 25692 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 2006, 8588, 25692 is 2.
HCF(2006, 8588, 25692) = 2
HCF of 2006, 8588, 25692 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2006, 8588, 25692 is 2.
Highest Common Factor of 2006,8588,25692 is 2
Step 1: Since 8588 > 2006, we apply the division lemma to 8588 and 2006, to get
8588 = 2006 x 4 + 564
Step 2: Since the reminder 2006 ≠ 0, we apply division lemma to 564 and 2006, to get
2006 = 564 x 3 + 314
Step 3: We consider the new divisor 564 and the new remainder 314, and apply the division lemma to get
564 = 314 x 1 + 250
We consider the new divisor 314 and the new remainder 250,and apply the division lemma to get
314 = 250 x 1 + 64
We consider the new divisor 250 and the new remainder 64,and apply the division lemma to get
250 = 64 x 3 + 58
We consider the new divisor 64 and the new remainder 58,and apply the division lemma to get
64 = 58 x 1 + 6
We consider the new divisor 58 and the new remainder 6,and apply the division lemma to get
58 = 6 x 9 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2006 and 8588 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(58,6) = HCF(64,58) = HCF(250,64) = HCF(314,250) = HCF(564,314) = HCF(2006,564) = HCF(8588,2006) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 25692 > 2, we apply the division lemma to 25692 and 2, to get
25692 = 2 x 12846 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 25692 is 2
Notice that 2 = HCF(25692,2) .
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Frequently Asked Questions on HCF of 2006, 8588, 25692 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 2006, 8588, 25692?
Answer: HCF of 2006, 8588, 25692 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2006, 8588, 25692 using Euclid's Algorithm?
Answer: For arbitrary numbers 2006, 8588, 25692 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.