Highest Common Factor of 772, 2171, 8307 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 772, 2171, 8307 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 772, 2171, 8307 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 772, 2171, 8307 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 772, 2171, 8307 is 1.
HCF(772, 2171, 8307) = 1
HCF of 772, 2171, 8307 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 772, 2171, 8307 is 1.
Highest Common Factor of 772,2171,8307 is 1
Step 1: Since 2171 > 772, we apply the division lemma to 2171 and 772, to get
2171 = 772 x 2 + 627
Step 2: Since the reminder 772 ≠ 0, we apply division lemma to 627 and 772, to get
772 = 627 x 1 + 145
Step 3: We consider the new divisor 627 and the new remainder 145, and apply the division lemma to get
627 = 145 x 4 + 47
We consider the new divisor 145 and the new remainder 47,and apply the division lemma to get
145 = 47 x 3 + 4
We consider the new divisor 47 and the new remainder 4,and apply the division lemma to get
47 = 4 x 11 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 772 and 2171 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(47,4) = HCF(145,47) = HCF(627,145) = HCF(772,627) = HCF(2171,772) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8307 > 1, we apply the division lemma to 8307 and 1, to get
8307 = 1 x 8307 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8307 is 1
Notice that 1 = HCF(8307,1) .
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Frequently Asked Questions on HCF of 772, 2171, 8307 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 772, 2171, 8307?
Answer: HCF of 772, 2171, 8307 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 772, 2171, 8307 using Euclid's Algorithm?
Answer: For arbitrary numbers 772, 2171, 8307 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.