Highest Common Factor of 514, 296, 414 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 514, 296, 414 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 514, 296, 414 is 2 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 514, 296, 414 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 514, 296, 414 is 2.
HCF(514, 296, 414) = 2
HCF of 514, 296, 414 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 514, 296, 414 is 2.
Highest Common Factor of 514,296,414 is 2
Step 1: Since 514 > 296, we apply the division lemma to 514 and 296, to get
514 = 296 x 1 + 218
Step 2: Since the reminder 296 ≠ 0, we apply division lemma to 218 and 296, to get
296 = 218 x 1 + 78
Step 3: We consider the new divisor 218 and the new remainder 78, and apply the division lemma to get
218 = 78 x 2 + 62
We consider the new divisor 78 and the new remainder 62,and apply the division lemma to get
78 = 62 x 1 + 16
We consider the new divisor 62 and the new remainder 16,and apply the division lemma to get
62 = 16 x 3 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 514 and 296 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(62,16) = HCF(78,62) = HCF(218,78) = HCF(296,218) = HCF(514,296) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 414 > 2, we apply the division lemma to 414 and 2, to get
414 = 2 x 207 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 414 is 2
Notice that 2 = HCF(414,2) .
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Frequently Asked Questions on HCF of 514, 296, 414 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 514, 296, 414?
Answer: HCF of 514, 296, 414 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 514, 296, 414 using Euclid's Algorithm?
Answer: For arbitrary numbers 514, 296, 414 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
