Highest Common Factor of 515, 330, 58 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 515, 330, 58 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 515, 330, 58 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 515, 330, 58 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 515, 330, 58 is 1.

HCF(515, 330, 58) = 1

HCF of 515, 330, 58 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 515, 330, 58 is 1.

Highest Common Factor of 515,330,58 using Euclid's algorithm

Highest Common Factor of 515,330,58 is 1

Step 1: Since 515 > 330, we apply the division lemma to 515 and 330, to get

515 = 330 x 1 + 185

Step 2: Since the reminder 330 ≠ 0, we apply division lemma to 185 and 330, to get

330 = 185 x 1 + 145

Step 3: We consider the new divisor 185 and the new remainder 145, and apply the division lemma to get

185 = 145 x 1 + 40

We consider the new divisor 145 and the new remainder 40,and apply the division lemma to get

145 = 40 x 3 + 25

We consider the new divisor 40 and the new remainder 25,and apply the division lemma to get

40 = 25 x 1 + 15

We consider the new divisor 25 and the new remainder 15,and apply the division lemma to get

25 = 15 x 1 + 10

We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get

15 = 10 x 1 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 515 and 330 is 5

Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(25,15) = HCF(40,25) = HCF(145,40) = HCF(185,145) = HCF(330,185) = HCF(515,330) .

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

Step 1: Since 58 > 5, we apply the division lemma to 58 and 5, to get

58 = 5 x 11 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: 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 5 and 58 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(58,5) .

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Frequently Asked Questions on HCF of 515, 330, 58 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 515, 330, 58?

Answer: HCF of 515, 330, 58 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 515, 330, 58 using Euclid's Algorithm?

Answer: For arbitrary numbers 515, 330, 58 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.