Highest Common Factor of 108, 301, 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 108, 301, 514 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 108, 301, 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 108, 301, 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 108, 301, 514 is 1.
HCF(108, 301, 514) = 1
HCF of 108, 301, 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 108, 301, 514 is 1.
Highest Common Factor of 108,301,514 is 1
Step 1: Since 301 > 108, we apply the division lemma to 301 and 108, to get
301 = 108 x 2 + 85
Step 2: Since the reminder 108 ≠ 0, we apply division lemma to 85 and 108, to get
108 = 85 x 1 + 23
Step 3: We consider the new divisor 85 and the new remainder 23, and apply the division lemma to get
85 = 23 x 3 + 16
We consider the new divisor 23 and the new remainder 16,and apply the division lemma to get
23 = 16 x 1 + 7
We consider the new divisor 16 and the new remainder 7,and apply the division lemma to get
16 = 7 x 2 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 108 and 301 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(16,7) = HCF(23,16) = HCF(85,23) = HCF(108,85) = HCF(301,108) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 514 > 1, we apply the division lemma to 514 and 1, to get
514 = 1 x 514 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 514 is 1
Notice that 1 = HCF(514,1) .
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Frequently Asked Questions on HCF of 108, 301, 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 108, 301, 514?
Answer: HCF of 108, 301, 514 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 108, 301, 514 using Euclid's Algorithm?
Answer: For arbitrary numbers 108, 301, 514 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.