Highest Common Factor of 7851, 667 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 7851, 667 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 7851, 667 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 7851, 667 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 7851, 667 is 1.
HCF(7851, 667) = 1
HCF of 7851, 667 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7851, 667 is 1.
Highest Common Factor of 7851,667 is 1
Step 1: Since 7851 > 667, we apply the division lemma to 7851 and 667, to get
7851 = 667 x 11 + 514
Step 2: Since the reminder 667 ≠ 0, we apply division lemma to 514 and 667, to get
667 = 514 x 1 + 153
Step 3: We consider the new divisor 514 and the new remainder 153, and apply the division lemma to get
514 = 153 x 3 + 55
We consider the new divisor 153 and the new remainder 55,and apply the division lemma to get
153 = 55 x 2 + 43
We consider the new divisor 55 and the new remainder 43,and apply the division lemma to get
55 = 43 x 1 + 12
We consider the new divisor 43 and the new remainder 12,and apply the division lemma to get
43 = 12 x 3 + 7
We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get
12 = 7 x 1 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 7851 and 667 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(43,12) = HCF(55,43) = HCF(153,55) = HCF(514,153) = HCF(667,514) = HCF(7851,667) .
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Frequently Asked Questions on HCF of 7851, 667 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 7851, 667?
Answer: HCF of 7851, 667 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7851, 667 using Euclid's Algorithm?
Answer: For arbitrary numbers 7851, 667 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.