Highest Common Factor of 2018, 2704 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 2018, 2704 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2018, 2704 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 2018, 2704 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 2018, 2704 is 2.
HCF(2018, 2704) = 2
HCF of 2018, 2704 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2018, 2704 is 2.
Highest Common Factor of 2018,2704 is 2
Step 1: Since 2704 > 2018, we apply the division lemma to 2704 and 2018, to get
2704 = 2018 x 1 + 686
Step 2: Since the reminder 2018 ≠ 0, we apply division lemma to 686 and 2018, to get
2018 = 686 x 2 + 646
Step 3: We consider the new divisor 686 and the new remainder 646, and apply the division lemma to get
686 = 646 x 1 + 40
We consider the new divisor 646 and the new remainder 40,and apply the division lemma to get
646 = 40 x 16 + 6
We consider the new divisor 40 and the new remainder 6,and apply the division lemma to get
40 = 6 x 6 + 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 2018 and 2704 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(40,6) = HCF(646,40) = HCF(686,646) = HCF(2018,686) = HCF(2704,2018) .
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Frequently Asked Questions on HCF of 2018, 2704 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 2018, 2704?
Answer: HCF of 2018, 2704 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2018, 2704 using Euclid's Algorithm?
Answer: For arbitrary numbers 2018, 2704 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.