Highest Common Factor of 780, 592, 514 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 780, 592, 514 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 780, 592, 514 is 2 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 780, 592, 514 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 780, 592, 514 is 2.

HCF(780, 592, 514) = 2

HCF of 780, 592, 514 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 780, 592, 514 is 2.

Highest Common Factor of 780,592,514 using Euclid's algorithm

Highest Common Factor of 780,592,514 is 2

Step 1: Since 780 > 592, we apply the division lemma to 780 and 592, to get

780 = 592 x 1 + 188

Step 2: Since the reminder 592 ≠ 0, we apply division lemma to 188 and 592, to get

592 = 188 x 3 + 28

Step 3: We consider the new divisor 188 and the new remainder 28, and apply the division lemma to get

188 = 28 x 6 + 20

We consider the new divisor 28 and the new remainder 20,and apply the division lemma to get

28 = 20 x 1 + 8

We consider the new divisor 20 and the new remainder 8,and apply the division lemma to get

20 = 8 x 2 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 780 and 592 is 4

Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(28,20) = HCF(188,28) = HCF(592,188) = HCF(780,592) .

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

Step 1: Since 514 > 4, we apply the division lemma to 514 and 4, to get

514 = 4 x 128 + 2

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 514 is 2

Notice that 2 = HCF(4,2) = HCF(514,4) .

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Frequently Asked Questions on HCF of 780, 592, 514 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 780, 592, 514?

Answer: HCF of 780, 592, 514 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 780, 592, 514 using Euclid's Algorithm?

Answer: For arbitrary numbers 780, 592, 514 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.