Highest Common Factor of 516, 999, 107 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 516, 999, 107 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 516, 999, 107 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 516, 999, 107 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 516, 999, 107 is 1.
HCF(516, 999, 107) = 1
HCF of 516, 999, 107 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 516, 999, 107 is 1.
Highest Common Factor of 516,999,107 is 1
Step 1: Since 999 > 516, we apply the division lemma to 999 and 516, to get
999 = 516 x 1 + 483
Step 2: Since the reminder 516 ≠ 0, we apply division lemma to 483 and 516, to get
516 = 483 x 1 + 33
Step 3: We consider the new divisor 483 and the new remainder 33, and apply the division lemma to get
483 = 33 x 14 + 21
We consider the new divisor 33 and the new remainder 21,and apply the division lemma to get
33 = 21 x 1 + 12
We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get
21 = 12 x 1 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 516 and 999 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(33,21) = HCF(483,33) = HCF(516,483) = HCF(999,516) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 107 > 3, we apply the division lemma to 107 and 3, to get
107 = 3 x 35 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 107 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(107,3) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 516, 999, 107 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 516, 999, 107?
Answer: HCF of 516, 999, 107 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 516, 999, 107 using Euclid's Algorithm?
Answer: For arbitrary numbers 516, 999, 107 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.