Highest Common Factor of 2055, 2768 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 2055, 2768 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2055, 2768 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 2055, 2768 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 2055, 2768 is 1.
HCF(2055, 2768) = 1
HCF of 2055, 2768 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2055, 2768 is 1.
Highest Common Factor of 2055,2768 is 1
Step 1: Since 2768 > 2055, we apply the division lemma to 2768 and 2055, to get
2768 = 2055 x 1 + 713
Step 2: Since the reminder 2055 ≠ 0, we apply division lemma to 713 and 2055, to get
2055 = 713 x 2 + 629
Step 3: We consider the new divisor 713 and the new remainder 629, and apply the division lemma to get
713 = 629 x 1 + 84
We consider the new divisor 629 and the new remainder 84,and apply the division lemma to get
629 = 84 x 7 + 41
We consider the new divisor 84 and the new remainder 41,and apply the division lemma to get
84 = 41 x 2 + 2
We consider the new divisor 41 and the new remainder 2,and apply the division lemma to get
41 = 2 x 20 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2055 and 2768 is 1
Notice that 1 = HCF(2,1) = HCF(41,2) = HCF(84,41) = HCF(629,84) = HCF(713,629) = HCF(2055,713) = HCF(2768,2055) .
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Frequently Asked Questions on HCF of 2055, 2768 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 2055, 2768?
Answer: HCF of 2055, 2768 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2055, 2768 using Euclid's Algorithm?
Answer: For arbitrary numbers 2055, 2768 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.