Highest Common Factor of 353, 497 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 353, 497 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 353, 497 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 353, 497 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 353, 497 is 1.

HCF(353, 497) = 1

HCF of 353, 497 using Euclid's algorithm

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

HCF of:

Highest common factor (HCF) of 353, 497 is 1.

Highest Common Factor of 353,497 using Euclid's algorithm

Highest Common Factor of 353,497 is 1

Step 1: Since 497 > 353, we apply the division lemma to 497 and 353, to get

497 = 353 x 1 + 144

Step 2: Since the reminder 353 ≠ 0, we apply division lemma to 144 and 353, to get

353 = 144 x 2 + 65

Step 3: We consider the new divisor 144 and the new remainder 65, and apply the division lemma to get

144 = 65 x 2 + 14

We consider the new divisor 65 and the new remainder 14,and apply the division lemma to get

65 = 14 x 4 + 9

We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get

14 = 9 x 1 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 353 and 497 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(65,14) = HCF(144,65) = HCF(353,144) = HCF(497,353) .

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Frequently Asked Questions on HCF of 353, 497 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 353, 497?

Answer: HCF of 353, 497 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 353, 497 using Euclid's Algorithm?

Answer: For arbitrary numbers 353, 497 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.