Highest Common Factor of 113, 3514, 5872 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 113, 3514, 5872 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 113, 3514, 5872 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 113, 3514, 5872 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 113, 3514, 5872 is 1.
HCF(113, 3514, 5872) = 1
HCF of 113, 3514, 5872 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 113, 3514, 5872 is 1.
Highest Common Factor of 113,3514,5872 is 1
Step 1: Since 3514 > 113, we apply the division lemma to 3514 and 113, to get
3514 = 113 x 31 + 11
Step 2: Since the reminder 113 ≠ 0, we apply division lemma to 11 and 113, to get
113 = 11 x 10 + 3
Step 3: We consider the new divisor 11 and the new remainder 3, and apply the division lemma to get
11 = 3 x 3 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 113 and 3514 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(113,11) = HCF(3514,113) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 5872 > 1, we apply the division lemma to 5872 and 1, to get
5872 = 1 x 5872 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 5872 is 1
Notice that 1 = HCF(5872,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 113, 3514, 5872 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 113, 3514, 5872?
Answer: HCF of 113, 3514, 5872 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 113, 3514, 5872 using Euclid's Algorithm?
Answer: For arbitrary numbers 113, 3514, 5872 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.