Highest Common Factor of 286, 353 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 286, 353 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 286, 353 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 286, 353 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 286, 353 is 1.

HCF(286, 353) = 1

HCF of 286, 353 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 286, 353 is 1.

Highest Common Factor of 286,353 using Euclid's algorithm

Highest Common Factor of 286,353 is 1

Step 1: Since 353 > 286, we apply the division lemma to 353 and 286, to get

353 = 286 x 1 + 67

Step 2: Since the reminder 286 ≠ 0, we apply division lemma to 67 and 286, to get

286 = 67 x 4 + 18

Step 3: We consider the new divisor 67 and the new remainder 18, and apply the division lemma to get

67 = 18 x 3 + 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 286 and 353 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(67,18) = HCF(286,67) = HCF(353,286) .

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Frequently Asked Questions on HCF of 286, 353 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 286, 353?

Answer: HCF of 286, 353 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 286, 353 using Euclid's Algorithm?

Answer: For arbitrary numbers 286, 353 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.