Highest Common Factor of 920, 588 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 920, 588 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 920, 588 is 4 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 920, 588 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 920, 588 is 4.

HCF(920, 588) = 4

HCF of 920, 588 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 920, 588 is 4.

Highest Common Factor of 920,588 using Euclid's algorithm

Highest Common Factor of 920,588 is 4

Step 1: Since 920 > 588, we apply the division lemma to 920 and 588, to get

920 = 588 x 1 + 332

Step 2: Since the reminder 588 ≠ 0, we apply division lemma to 332 and 588, to get

588 = 332 x 1 + 256

Step 3: We consider the new divisor 332 and the new remainder 256, and apply the division lemma to get

332 = 256 x 1 + 76

We consider the new divisor 256 and the new remainder 76,and apply the division lemma to get

256 = 76 x 3 + 28

We consider the new divisor 76 and the new remainder 28,and apply the division lemma to get

76 = 28 x 2 + 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 920 and 588 is 4

Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(28,20) = HCF(76,28) = HCF(256,76) = HCF(332,256) = HCF(588,332) = HCF(920,588) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 920, 588 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 920, 588?

Answer: HCF of 920, 588 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 920, 588 using Euclid's Algorithm?

Answer: For arbitrary numbers 920, 588 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.