Highest Common Factor of 975, 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 975, 920, 588 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 975, 920, 588 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 975, 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 975, 920, 588 is 1.

HCF(975, 920, 588) = 1

HCF of 975, 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 975, 920, 588 is 1.

Highest Common Factor of 975,920,588 using Euclid's algorithm

Highest Common Factor of 975,920,588 is 1

Step 1: Since 975 > 920, we apply the division lemma to 975 and 920, to get

975 = 920 x 1 + 55

Step 2: Since the reminder 920 ≠ 0, we apply division lemma to 55 and 920, to get

920 = 55 x 16 + 40

Step 3: We consider the new divisor 55 and the new remainder 40, and apply the division lemma to get

55 = 40 x 1 + 15

We consider the new divisor 40 and the new remainder 15,and apply the division lemma to get

40 = 15 x 2 + 10

We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get

15 = 10 x 1 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 975 and 920 is 5

Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(40,15) = HCF(55,40) = HCF(920,55) = HCF(975,920) .

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

Step 1: Since 588 > 5, we apply the division lemma to 588 and 5, to get

588 = 5 x 117 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 588 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(588,5) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 975, 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 975, 920, 588?

Answer: HCF of 975, 920, 588 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 975, 920, 588 using Euclid's Algorithm?

Answer: For arbitrary numbers 975, 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.