Highest Common Factor of 851, 2678 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 851, 2678 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 851, 2678 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 851, 2678 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 851, 2678 is 1.
HCF(851, 2678) = 1
HCF of 851, 2678 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 851, 2678 is 1.
Highest Common Factor of 851,2678 is 1
Step 1: Since 2678 > 851, we apply the division lemma to 2678 and 851, to get
2678 = 851 x 3 + 125
Step 2: Since the reminder 851 ≠ 0, we apply division lemma to 125 and 851, to get
851 = 125 x 6 + 101
Step 3: We consider the new divisor 125 and the new remainder 101, and apply the division lemma to get
125 = 101 x 1 + 24
We consider the new divisor 101 and the new remainder 24,and apply the division lemma to get
101 = 24 x 4 + 5
We consider the new divisor 24 and the new remainder 5,and apply the division lemma to get
24 = 5 x 4 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 851 and 2678 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(24,5) = HCF(101,24) = HCF(125,101) = HCF(851,125) = HCF(2678,851) .
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Frequently Asked Questions on HCF of 851, 2678 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 851, 2678?
Answer: HCF of 851, 2678 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 851, 2678 using Euclid's Algorithm?
Answer: For arbitrary numbers 851, 2678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.