Highest Common Factor of 351, 512 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 351, 512 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 351, 512 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 351, 512 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 351, 512 is 1.

HCF(351, 512) = 1

HCF of 351, 512 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 351, 512 is 1.

Highest Common Factor of 351,512 using Euclid's algorithm

Highest Common Factor of 351,512 is 1

Step 1: Since 512 > 351, we apply the division lemma to 512 and 351, to get

512 = 351 x 1 + 161

Step 2: Since the reminder 351 ≠ 0, we apply division lemma to 161 and 351, to get

351 = 161 x 2 + 29

Step 3: We consider the new divisor 161 and the new remainder 29, and apply the division lemma to get

161 = 29 x 5 + 16

We consider the new divisor 29 and the new remainder 16,and apply the division lemma to get

29 = 16 x 1 + 13

We consider the new divisor 16 and the new remainder 13,and apply the division lemma to get

16 = 13 x 1 + 3

We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get

13 = 3 x 4 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 351 and 512 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(29,16) = HCF(161,29) = HCF(351,161) = HCF(512,351) .

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Frequently Asked Questions on HCF of 351, 512 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 351, 512?

Answer: HCF of 351, 512 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 351, 512 using Euclid's Algorithm?

Answer: For arbitrary numbers 351, 512 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.