Highest Common Factor of 493, 302 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 493, 302 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 493, 302 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 493, 302 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 493, 302 is 1.
HCF(493, 302) = 1
HCF of 493, 302 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 493, 302 is 1.
Highest Common Factor of 493,302 is 1
Step 1: Since 493 > 302, we apply the division lemma to 493 and 302, to get
493 = 302 x 1 + 191
Step 2: Since the reminder 302 ≠ 0, we apply division lemma to 191 and 302, to get
302 = 191 x 1 + 111
Step 3: We consider the new divisor 191 and the new remainder 111, and apply the division lemma to get
191 = 111 x 1 + 80
We consider the new divisor 111 and the new remainder 80,and apply the division lemma to get
111 = 80 x 1 + 31
We consider the new divisor 80 and the new remainder 31,and apply the division lemma to get
80 = 31 x 2 + 18
We consider the new divisor 31 and the new remainder 18,and apply the division lemma to get
31 = 18 x 1 + 13
We consider the new divisor 18 and the new remainder 13,and apply the division lemma to get
18 = 13 x 1 + 5
We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get
13 = 5 x 2 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 493 and 302 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(31,18) = HCF(80,31) = HCF(111,80) = HCF(191,111) = HCF(302,191) = HCF(493,302) .
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Frequently Asked Questions on HCF of 493, 302 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 493, 302?
Answer: HCF of 493, 302 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 493, 302 using Euclid's Algorithm?
Answer: For arbitrary numbers 493, 302 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
