Highest Common Factor of 302, 413 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 302, 413 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 302, 413 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 302, 413 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 302, 413 is 1.

HCF(302, 413) = 1

HCF of 302, 413 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 302, 413 is 1.

Highest Common Factor of 302,413 using Euclid's algorithm

Highest Common Factor of 302,413 is 1

Step 1: Since 413 > 302, we apply the division lemma to 413 and 302, to get

413 = 302 x 1 + 111

Step 2: Since the reminder 302 ≠ 0, we apply division lemma to 111 and 302, to get

302 = 111 x 2 + 80

Step 3: 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 302 and 413 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(302,111) = HCF(413,302) .

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Frequently Asked Questions on HCF of 302, 413 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 302, 413?

Answer: HCF of 302, 413 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 302, 413 using Euclid's Algorithm?

Answer: For arbitrary numbers 302, 413 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.