Highest Common Factor of 512, 852, 570 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 512, 852, 570 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 512, 852, 570 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 512, 852, 570 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 512, 852, 570 is 2.

HCF(512, 852, 570) = 2

HCF of 512, 852, 570 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 512, 852, 570 is 2.

Highest Common Factor of 512,852,570 using Euclid's algorithm

Highest Common Factor of 512,852,570 is 2

Step 1: Since 852 > 512, we apply the division lemma to 852 and 512, to get

852 = 512 x 1 + 340

Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 340 and 512, to get

512 = 340 x 1 + 172

Step 3: We consider the new divisor 340 and the new remainder 172, and apply the division lemma to get

340 = 172 x 1 + 168

We consider the new divisor 172 and the new remainder 168,and apply the division lemma to get

172 = 168 x 1 + 4

We consider the new divisor 168 and the new remainder 4,and apply the division lemma to get

168 = 4 x 42 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 512 and 852 is 4

Notice that 4 = HCF(168,4) = HCF(172,168) = HCF(340,172) = HCF(512,340) = HCF(852,512) .

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

Step 1: Since 570 > 4, we apply the division lemma to 570 and 4, to get

570 = 4 x 142 + 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 570 is 2

Notice that 2 = HCF(4,2) = HCF(570,4) .

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Frequently Asked Questions on HCF of 512, 852, 570 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 512, 852, 570?

Answer: HCF of 512, 852, 570 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 512, 852, 570 using Euclid's Algorithm?

Answer: For arbitrary numbers 512, 852, 570 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.