How to Find GCF of 825/510, 8142/2803?

GCF of 825/510, 8142/2803

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 825/510, 8142/2803 i.e 3/1429530 easily. The following is the detailed procedure to determine the greatest common factor of fractions 825/510, 8142/2803.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 825/510,8142/2803?

Given fractions are 825/510,8142/2803

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 825/510,8142/2803, numerators are 825,8142

Denominators are 510,2803

The GCF of 825,8142 is 3 .

LCM of 510,2803 is 1429530.

The greatest common factor of 825/510,8142/2803 = [GCF of 825,8142]/[LCM of 510,2803]= 3/1429530

Therefore, the GCF of 825/510,8142/2803 is 3/1429530.

Greatest Common Factor of 825,8142

To find the highest common factor of 825,8142, we have to find the factors of both numbers and list the highest common factor.

The factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825

The factors of 8142 are 1, 2, 3, 6, 23, 46, 59, 69, 118, 138, 177, 354, 1357, 2714, 4071, 8142

The HCF of 825,8142 is 3.

Lets's calculate GCF of 825,8142

Greatest Common Factor (GCF) of 825,8142 By Common Division

3	825, 8142
	275, 2714

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 825,8142 By Matching Biggest Common Factor Method

Now, list down the factors of 825

1,3,5,11,15,25,33,55,75,165,275,825

Now, list down the factors of 8142

1,2,3,6,23,46,59,69,118,138,177,354,1357,2714,4071,8142

Greatest Common Factor

We found the factors 825,8142 . The biggest common factor number is the GCF number.
So the greatest common factor 825,8142 is 3.

Lets's calculate LCM of 510,2803

Lowest Common Multiple of 510,2803 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1429530

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1429530

Therefore, the GCF of Fractions 825/510,8142/2803 is 3/1429530

Least Common Multiple of 510,2803 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 510,2803 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(510,2803) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(510,2803) x common factors =1 x 1 = 1

LCM(510,2803) = ( 510 × 2803 ) / 1

LCM(510,2803) = 1429530 / 1

LCM(510,2803) = 1429530

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 825/510, 8142/2803

1. What is the HCF of 825,8142?

The HCF of 825,8142 is 3

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 825/510, 8142/2803?

Answer: GCF of Numerators as per given numbers 825/510, 8142/2803 is

GCF of Numerators i.e. for 825,8142 is 3

LCM of denominators i.e. for 510,2803 is 1429530.

Thus, GCF of Fractions is 3/1429530.Finally, GCF of Fractions for 825/510, 8142/2803 is 3/1429530.