Highest Common Factor of 414, 645, 514 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 414, 645, 514 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 414, 645, 514 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 414, 645, 514 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 414, 645, 514 is 1.
HCF(414, 645, 514) = 1
HCF of 414, 645, 514 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 414, 645, 514 is 1.
Highest Common Factor of 414,645,514 is 1
Step 1: Since 645 > 414, we apply the division lemma to 645 and 414, to get
645 = 414 x 1 + 231
Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 231 and 414, to get
414 = 231 x 1 + 183
Step 3: We consider the new divisor 231 and the new remainder 183, and apply the division lemma to get
231 = 183 x 1 + 48
We consider the new divisor 183 and the new remainder 48,and apply the division lemma to get
183 = 48 x 3 + 39
We consider the new divisor 48 and the new remainder 39,and apply the division lemma to get
48 = 39 x 1 + 9
We consider the new divisor 39 and the new remainder 9,and apply the division lemma to get
39 = 9 x 4 + 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 414 and 645 is 3
Notice that 3 = HCF(9,3) = HCF(39,9) = HCF(48,39) = HCF(183,48) = HCF(231,183) = HCF(414,231) = HCF(645,414) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 514 > 3, we apply the division lemma to 514 and 3, to get
514 = 3 x 171 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 514 is 1
Notice that 1 = HCF(3,1) = HCF(514,3) .
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Frequently Asked Questions on HCF of 414, 645, 514 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 414, 645, 514?
Answer: HCF of 414, 645, 514 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 414, 645, 514 using Euclid's Algorithm?
Answer: For arbitrary numbers 414, 645, 514 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
