Highest Common Factor of 314, 517, 20 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 314, 517, 20 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 314, 517, 20 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 314, 517, 20 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 314, 517, 20 is 1.
HCF(314, 517, 20) = 1
HCF of 314, 517, 20 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 314, 517, 20 is 1.
Highest Common Factor of 314,517,20 is 1
Step 1: Since 517 > 314, we apply the division lemma to 517 and 314, to get
517 = 314 x 1 + 203
Step 2: Since the reminder 314 ≠ 0, we apply division lemma to 203 and 314, to get
314 = 203 x 1 + 111
Step 3: We consider the new divisor 203 and the new remainder 111, and apply the division lemma to get
203 = 111 x 1 + 92
We consider the new divisor 111 and the new remainder 92,and apply the division lemma to get
111 = 92 x 1 + 19
We consider the new divisor 92 and the new remainder 19,and apply the division lemma to get
92 = 19 x 4 + 16
We consider the new divisor 19 and the new remainder 16,and apply the division lemma to get
19 = 16 x 1 + 3
We consider the new divisor 16 and the new remainder 3,and apply the division lemma to get
16 = 3 x 5 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 314 and 517 is 1
Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(19,16) = HCF(92,19) = HCF(111,92) = HCF(203,111) = HCF(314,203) = HCF(517,314) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 20 > 1, we apply the division lemma to 20 and 1, to get
20 = 1 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 20 is 1
Notice that 1 = HCF(20,1) .
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Frequently Asked Questions on HCF of 314, 517, 20 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 314, 517, 20?
Answer: HCF of 314, 517, 20 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 314, 517, 20 using Euclid's Algorithm?
Answer: For arbitrary numbers 314, 517, 20 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.