Highest Common Factor of 513, 876 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 513, 876 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 513, 876 is 3 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 513, 876 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 513, 876 is 3.
HCF(513, 876) = 3
HCF of 513, 876 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 513, 876 is 3.
Highest Common Factor of 513,876 is 3
Step 1: Since 876 > 513, we apply the division lemma to 876 and 513, to get
876 = 513 x 1 + 363
Step 2: Since the reminder 513 ≠ 0, we apply division lemma to 363 and 513, to get
513 = 363 x 1 + 150
Step 3: We consider the new divisor 363 and the new remainder 150, and apply the division lemma to get
363 = 150 x 2 + 63
We consider the new divisor 150 and the new remainder 63,and apply the division lemma to get
150 = 63 x 2 + 24
We consider the new divisor 63 and the new remainder 24,and apply the division lemma to get
63 = 24 x 2 + 15
We consider the new divisor 24 and the new remainder 15,and apply the division lemma to get
24 = 15 x 1 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 513 and 876 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(24,15) = HCF(63,24) = HCF(150,63) = HCF(363,150) = HCF(513,363) = HCF(876,513) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 513, 876 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 513, 876?
Answer: HCF of 513, 876 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 513, 876 using Euclid's Algorithm?
Answer: For arbitrary numbers 513, 876 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.