Highest Common Factor of 516, 289, 75 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 516, 289, 75 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 516, 289, 75 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 516, 289, 75 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 516, 289, 75 is 1.

HCF(516, 289, 75) = 1

HCF of 516, 289, 75 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 516, 289, 75 is 1.

Highest Common Factor of 516,289,75 using Euclid's algorithm

Highest Common Factor of 516,289,75 is 1

Step 1: Since 516 > 289, we apply the division lemma to 516 and 289, to get

516 = 289 x 1 + 227

Step 2: Since the reminder 289 ≠ 0, we apply division lemma to 227 and 289, to get

289 = 227 x 1 + 62

Step 3: We consider the new divisor 227 and the new remainder 62, and apply the division lemma to get

227 = 62 x 3 + 41

We consider the new divisor 62 and the new remainder 41,and apply the division lemma to get

62 = 41 x 1 + 21

We consider the new divisor 41 and the new remainder 21,and apply the division lemma to get

41 = 21 x 1 + 20

We consider the new divisor 21 and the new remainder 20,and apply the division lemma to get

21 = 20 x 1 + 1

We consider the new divisor 20 and the new remainder 1,and apply the division lemma to get

20 = 1 x 20 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 516 and 289 is 1

Notice that 1 = HCF(20,1) = HCF(21,20) = HCF(41,21) = HCF(62,41) = HCF(227,62) = HCF(289,227) = HCF(516,289) .

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

Step 1: Since 75 > 1, we apply the division lemma to 75 and 1, to get

75 = 1 x 75 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 75 is 1

Notice that 1 = HCF(75,1) .

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Frequently Asked Questions on HCF of 516, 289, 75 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 516, 289, 75?

Answer: HCF of 516, 289, 75 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 516, 289, 75 using Euclid's Algorithm?

Answer: For arbitrary numbers 516, 289, 75 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.