Highest Common Factor of 301, 491 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 301, 491 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 301, 491 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 301, 491 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 301, 491 is 1.
HCF(301, 491) = 1
HCF of 301, 491 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 301, 491 is 1.
Highest Common Factor of 301,491 is 1
Step 1: Since 491 > 301, we apply the division lemma to 491 and 301, to get
491 = 301 x 1 + 190
Step 2: Since the reminder 301 ≠ 0, we apply division lemma to 190 and 301, to get
301 = 190 x 1 + 111
Step 3: We consider the new divisor 190 and the new remainder 111, and apply the division lemma to get
190 = 111 x 1 + 79
We consider the new divisor 111 and the new remainder 79,and apply the division lemma to get
111 = 79 x 1 + 32
We consider the new divisor 79 and the new remainder 32,and apply the division lemma to get
79 = 32 x 2 + 15
We consider the new divisor 32 and the new remainder 15,and apply the division lemma to get
32 = 15 x 2 + 2
We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get
15 = 2 x 7 + 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 301 and 491 is 1
Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(32,15) = HCF(79,32) = HCF(111,79) = HCF(190,111) = HCF(301,190) = HCF(491,301) .
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Frequently Asked Questions on HCF of 301, 491 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 301, 491?
Answer: HCF of 301, 491 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 301, 491 using Euclid's Algorithm?
Answer: For arbitrary numbers 301, 491 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.