Highest Common Factor of 513, 820, 354 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 513, 820, 354 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 513, 820, 354 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 513, 820, 354 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 513, 820, 354 is 1.

HCF(513, 820, 354) = 1

HCF of 513, 820, 354 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 513, 820, 354 is 1.

Highest Common Factor of 513,820,354 using Euclid's algorithm

Highest Common Factor of 513,820,354 is 1

Step 1: Since 820 > 513, we apply the division lemma to 820 and 513, to get

820 = 513 x 1 + 307

Step 2: Since the reminder 513 ≠ 0, we apply division lemma to 307 and 513, to get

513 = 307 x 1 + 206

Step 3: We consider the new divisor 307 and the new remainder 206, and apply the division lemma to get

307 = 206 x 1 + 101

We consider the new divisor 206 and the new remainder 101,and apply the division lemma to get

206 = 101 x 2 + 4

We consider the new divisor 101 and the new remainder 4,and apply the division lemma to get

101 = 4 x 25 + 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 513 and 820 is 1

Notice that 1 = HCF(4,1) = HCF(101,4) = HCF(206,101) = HCF(307,206) = HCF(513,307) = HCF(820,513) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 354 > 1, we apply the division lemma to 354 and 1, to get

354 = 1 x 354 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 354 is 1

Notice that 1 = HCF(354,1) .

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Frequently Asked Questions on HCF of 513, 820, 354 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 513, 820, 354?

Answer: HCF of 513, 820, 354 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 513, 820, 354 using Euclid's Algorithm?

Answer: For arbitrary numbers 513, 820, 354 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.