Highest Common Factor of 712, 2722, 8454 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 712, 2722, 8454 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 712, 2722, 8454 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 712, 2722, 8454 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 712, 2722, 8454 is 2.
HCF(712, 2722, 8454) = 2
HCF of 712, 2722, 8454 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 712, 2722, 8454 is 2.
Highest Common Factor of 712,2722,8454 is 2
Step 1: Since 2722 > 712, we apply the division lemma to 2722 and 712, to get
2722 = 712 x 3 + 586
Step 2: Since the reminder 712 ≠ 0, we apply division lemma to 586 and 712, to get
712 = 586 x 1 + 126
Step 3: We consider the new divisor 586 and the new remainder 126, and apply the division lemma to get
586 = 126 x 4 + 82
We consider the new divisor 126 and the new remainder 82,and apply the division lemma to get
126 = 82 x 1 + 44
We consider the new divisor 82 and the new remainder 44,and apply the division lemma to get
82 = 44 x 1 + 38
We consider the new divisor 44 and the new remainder 38,and apply the division lemma to get
44 = 38 x 1 + 6
We consider the new divisor 38 and the new remainder 6,and apply the division lemma to get
38 = 6 x 6 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 712 and 2722 is 2
Notice that 2 = HCF(6,2) = HCF(38,6) = HCF(44,38) = HCF(82,44) = HCF(126,82) = HCF(586,126) = HCF(712,586) = HCF(2722,712) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8454 > 2, we apply the division lemma to 8454 and 2, to get
8454 = 2 x 4227 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 8454 is 2
Notice that 2 = HCF(8454,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 712, 2722, 8454 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 712, 2722, 8454?
Answer: HCF of 712, 2722, 8454 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 712, 2722, 8454 using Euclid's Algorithm?
Answer: For arbitrary numbers 712, 2722, 8454 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.