Highest Common Factor of 827, 514, 69 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 827, 514, 69 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 827, 514, 69 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 827, 514, 69 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 827, 514, 69 is 1.
HCF(827, 514, 69) = 1
HCF of 827, 514, 69 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 827, 514, 69 is 1.
Highest Common Factor of 827,514,69 is 1
Step 1: Since 827 > 514, we apply the division lemma to 827 and 514, to get
827 = 514 x 1 + 313
Step 2: Since the reminder 514 ≠ 0, we apply division lemma to 313 and 514, to get
514 = 313 x 1 + 201
Step 3: We consider the new divisor 313 and the new remainder 201, and apply the division lemma to get
313 = 201 x 1 + 112
We consider the new divisor 201 and the new remainder 112,and apply the division lemma to get
201 = 112 x 1 + 89
We consider the new divisor 112 and the new remainder 89,and apply the division lemma to get
112 = 89 x 1 + 23
We consider the new divisor 89 and the new remainder 23,and apply the division lemma to get
89 = 23 x 3 + 20
We consider the new divisor 23 and the new remainder 20,and apply the division lemma to get
23 = 20 x 1 + 3
We consider the new divisor 20 and the new remainder 3,and apply the division lemma to get
20 = 3 x 6 + 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 827 and 514 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(20,3) = HCF(23,20) = HCF(89,23) = HCF(112,89) = HCF(201,112) = HCF(313,201) = HCF(514,313) = HCF(827,514) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 69 > 1, we apply the division lemma to 69 and 1, to get
69 = 1 x 69 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 69 is 1
Notice that 1 = HCF(69,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 827, 514, 69 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 827, 514, 69?
Answer: HCF of 827, 514, 69 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 827, 514, 69 using Euclid's Algorithm?
Answer: For arbitrary numbers 827, 514, 69 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
