Highest Common Factor of 824, 572, 675 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 824, 572, 675 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 824, 572, 675 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 824, 572, 675 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 824, 572, 675 is 1.

HCF(824, 572, 675) = 1

HCF of 824, 572, 675 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 824, 572, 675 is 1.

Highest Common Factor of 824,572,675 using Euclid's algorithm

Highest Common Factor of 824,572,675 is 1

Step 1: Since 824 > 572, we apply the division lemma to 824 and 572, to get

824 = 572 x 1 + 252

Step 2: Since the reminder 572 ≠ 0, we apply division lemma to 252 and 572, to get

572 = 252 x 2 + 68

Step 3: We consider the new divisor 252 and the new remainder 68, and apply the division lemma to get

252 = 68 x 3 + 48

We consider the new divisor 68 and the new remainder 48,and apply the division lemma to get

68 = 48 x 1 + 20

We consider the new divisor 48 and the new remainder 20,and apply the division lemma to get

48 = 20 x 2 + 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 824 and 572 is 4

Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(48,20) = HCF(68,48) = HCF(252,68) = HCF(572,252) = HCF(824,572) .

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

Step 1: Since 675 > 4, we apply the division lemma to 675 and 4, to get

675 = 4 x 168 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 675 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(675,4) .

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Frequently Asked Questions on HCF of 824, 572, 675 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 824, 572, 675?

Answer: HCF of 824, 572, 675 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 824, 572, 675 using Euclid's Algorithm?

Answer: For arbitrary numbers 824, 572, 675 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.