Highest Common Factor of 491, 314 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 491, 314 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 491, 314 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 491, 314 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 491, 314 is 1.
HCF(491, 314) = 1
HCF of 491, 314 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 491, 314 is 1.
Highest Common Factor of 491,314 is 1
Step 1: Since 491 > 314, we apply the division lemma to 491 and 314, to get
491 = 314 x 1 + 177
Step 2: Since the reminder 314 ≠ 0, we apply division lemma to 177 and 314, to get
314 = 177 x 1 + 137
Step 3: We consider the new divisor 177 and the new remainder 137, and apply the division lemma to get
177 = 137 x 1 + 40
We consider the new divisor 137 and the new remainder 40,and apply the division lemma to get
137 = 40 x 3 + 17
We consider the new divisor 40 and the new remainder 17,and apply the division lemma to get
40 = 17 x 2 + 6
We consider the new divisor 17 and the new remainder 6,and apply the division lemma to get
17 = 6 x 2 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 491 and 314 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(17,6) = HCF(40,17) = HCF(137,40) = HCF(177,137) = HCF(314,177) = HCF(491,314) .
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Frequently Asked Questions on HCF of 491, 314 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 491, 314?
Answer: HCF of 491, 314 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 491, 314 using Euclid's Algorithm?
Answer: For arbitrary numbers 491, 314 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.