Highest Common Factor of 516, 1955, 3414 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, 1955, 3414 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 516, 1955, 3414 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, 1955, 3414 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, 1955, 3414 is 1.
HCF(516, 1955, 3414) = 1
HCF of 516, 1955, 3414 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, 1955, 3414 is 1.
Highest Common Factor of 516,1955,3414 is 1
Step 1: Since 1955 > 516, we apply the division lemma to 1955 and 516, to get
1955 = 516 x 3 + 407
Step 2: Since the reminder 516 ≠ 0, we apply division lemma to 407 and 516, to get
516 = 407 x 1 + 109
Step 3: We consider the new divisor 407 and the new remainder 109, and apply the division lemma to get
407 = 109 x 3 + 80
We consider the new divisor 109 and the new remainder 80,and apply the division lemma to get
109 = 80 x 1 + 29
We consider the new divisor 80 and the new remainder 29,and apply the division lemma to get
80 = 29 x 2 + 22
We consider the new divisor 29 and the new remainder 22,and apply the division lemma to get
29 = 22 x 1 + 7
We consider the new divisor 22 and the new remainder 7,and apply the division lemma to get
22 = 7 x 3 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 516 and 1955 is 1
Notice that 1 = HCF(7,1) = HCF(22,7) = HCF(29,22) = HCF(80,29) = HCF(109,80) = HCF(407,109) = HCF(516,407) = HCF(1955,516) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3414 > 1, we apply the division lemma to 3414 and 1, to get
3414 = 1 x 3414 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 3414 is 1
Notice that 1 = HCF(3414,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 516, 1955, 3414 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, 1955, 3414?
Answer: HCF of 516, 1955, 3414 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 516, 1955, 3414 using Euclid's Algorithm?
Answer: For arbitrary numbers 516, 1955, 3414 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.