Highest Common Factor of 872, 460, 583 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 872, 460, 583 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 872, 460, 583 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 872, 460, 583 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 872, 460, 583 is 1.

HCF(872, 460, 583) = 1

HCF of 872, 460, 583 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 872, 460, 583 is 1.

Highest Common Factor of 872,460,583 using Euclid's algorithm

Highest Common Factor of 872,460,583 is 1

Step 1: Since 872 > 460, we apply the division lemma to 872 and 460, to get

872 = 460 x 1 + 412

Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 412 and 460, to get

460 = 412 x 1 + 48

Step 3: We consider the new divisor 412 and the new remainder 48, and apply the division lemma to get

412 = 48 x 8 + 28

We consider the new divisor 48 and the new remainder 28,and apply the division lemma to get

48 = 28 x 1 + 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 872 and 460 is 4

Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(28,20) = HCF(48,28) = HCF(412,48) = HCF(460,412) = HCF(872,460) .

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

Step 1: Since 583 > 4, we apply the division lemma to 583 and 4, to get

583 = 4 x 145 + 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 583 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(583,4) .

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Frequently Asked Questions on HCF of 872, 460, 583 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 872, 460, 583?

Answer: HCF of 872, 460, 583 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 872, 460, 583 using Euclid's Algorithm?

Answer: For arbitrary numbers 872, 460, 583 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.