Highest Common Factor of 514, 16872 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 514, 16872 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 514, 16872 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 514, 16872 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 514, 16872 is 2.
HCF(514, 16872) = 2
HCF of 514, 16872 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 514, 16872 is 2.
Highest Common Factor of 514,16872 is 2
Step 1: Since 16872 > 514, we apply the division lemma to 16872 and 514, to get
16872 = 514 x 32 + 424
Step 2: Since the reminder 514 ≠ 0, we apply division lemma to 424 and 514, to get
514 = 424 x 1 + 90
Step 3: We consider the new divisor 424 and the new remainder 90, and apply the division lemma to get
424 = 90 x 4 + 64
We consider the new divisor 90 and the new remainder 64,and apply the division lemma to get
90 = 64 x 1 + 26
We consider the new divisor 64 and the new remainder 26,and apply the division lemma to get
64 = 26 x 2 + 12
We consider the new divisor 26 and the new remainder 12,and apply the division lemma to get
26 = 12 x 2 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 514 and 16872 is 2
Notice that 2 = HCF(12,2) = HCF(26,12) = HCF(64,26) = HCF(90,64) = HCF(424,90) = HCF(514,424) = HCF(16872,514) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 514, 16872 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 514, 16872?
Answer: HCF of 514, 16872 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 514, 16872 using Euclid's Algorithm?
Answer: For arbitrary numbers 514, 16872 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.