Highest Common Factor of 513, 333, 348, 86 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, 333, 348, 86 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 513, 333, 348, 86 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, 333, 348, 86 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, 333, 348, 86 is 1.

HCF(513, 333, 348, 86) = 1

HCF of 513, 333, 348, 86 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, 333, 348, 86 is 1.

Highest Common Factor of 513,333,348,86 using Euclid's algorithm

Highest Common Factor of 513,333,348,86 is 1

Step 1: Since 513 > 333, we apply the division lemma to 513 and 333, to get

513 = 333 x 1 + 180

Step 2: Since the reminder 333 ≠ 0, we apply division lemma to 180 and 333, to get

333 = 180 x 1 + 153

Step 3: We consider the new divisor 180 and the new remainder 153, and apply the division lemma to get

180 = 153 x 1 + 27

We consider the new divisor 153 and the new remainder 27,and apply the division lemma to get

153 = 27 x 5 + 18

We consider the new divisor 27 and the new remainder 18,and apply the division lemma to get

27 = 18 x 1 + 9

We consider the new divisor 18 and the new remainder 9,and apply the division lemma to get

18 = 9 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 513 and 333 is 9

Notice that 9 = HCF(18,9) = HCF(27,18) = HCF(153,27) = HCF(180,153) = HCF(333,180) = HCF(513,333) .

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

Step 1: Since 348 > 9, we apply the division lemma to 348 and 9, to get

348 = 9 x 38 + 6

Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 6 and 9, to get

9 = 6 x 1 + 3

Step 3: We consider the new divisor 6 and the new remainder 3, and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9 and 348 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(348,9) .

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

Step 1: Since 86 > 3, we apply the division lemma to 86 and 3, to get

86 = 3 x 28 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 86 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(86,3) .

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Frequently Asked Questions on HCF of 513, 333, 348, 86 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, 333, 348, 86?

Answer: HCF of 513, 333, 348, 86 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 513, 333, 348, 86 using Euclid's Algorithm?

Answer: For arbitrary numbers 513, 333, 348, 86 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.