Highest Common Factor of 515, 665, 278, 814 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 515, 665, 278, 814 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 515, 665, 278, 814 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 515, 665, 278, 814 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 515, 665, 278, 814 is 1.
HCF(515, 665, 278, 814) = 1
HCF of 515, 665, 278, 814 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 515, 665, 278, 814 is 1.
Highest Common Factor of 515,665,278,814 is 1
Step 1: Since 665 > 515, we apply the division lemma to 665 and 515, to get
665 = 515 x 1 + 150
Step 2: Since the reminder 515 ≠ 0, we apply division lemma to 150 and 515, to get
515 = 150 x 3 + 65
Step 3: We consider the new divisor 150 and the new remainder 65, and apply the division lemma to get
150 = 65 x 2 + 20
We consider the new divisor 65 and the new remainder 20,and apply the division lemma to get
65 = 20 x 3 + 5
We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 515 and 665 is 5
Notice that 5 = HCF(20,5) = HCF(65,20) = HCF(150,65) = HCF(515,150) = HCF(665,515) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 278 > 5, we apply the division lemma to 278 and 5, to get
278 = 5 x 55 + 3
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get
5 = 3 x 1 + 2
Step 3: 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 5 and 278 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(278,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 814 > 1, we apply the division lemma to 814 and 1, to get
814 = 1 x 814 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 814 is 1
Notice that 1 = HCF(814,1) .
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Frequently Asked Questions on HCF of 515, 665, 278, 814 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 515, 665, 278, 814?
Answer: HCF of 515, 665, 278, 814 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 515, 665, 278, 814 using Euclid's Algorithm?
Answer: For arbitrary numbers 515, 665, 278, 814 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
