How to Find GCF of 6812/225, 1460/6563?

GCF of 6812/225, 1460/6563

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 6812/225, 1460/6563 i.e 4/1476675 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6812/225, 1460/6563.

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 6812/225,1460/6563?

Given fractions are 6812/225,1460/6563

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 6812/225,1460/6563, numerators are 6812,1460

Denominators are 225,6563

The GCF of 6812,1460 is 4 .

LCM of 225,6563 is 1476675.

The greatest common factor of 6812/225,1460/6563 = [GCF of 6812,1460]/[LCM of 225,6563]= 4/1476675

Therefore, the GCF of 6812/225,1460/6563 is 4/1476675.

Greatest Common Factor of 6812,1460

To find the highest common factor of 6812,1460, we have to find the factors of both numbers and list the highest common factor.

The factors of 6812 are 1, 2, 4, 13, 26, 52, 131, 262, 524, 1703, 3406, 6812

The factors of 1460 are 1, 2, 4, 5, 10, 20, 73, 146, 292, 365, 730, 1460

The HCF of 6812,1460 is 4.

Lets's calculate GCF of 6812,1460

Greatest Common Factor (GCF) of 6812,1460 By Common Division

2	6812, 1460
2	3406, 730
	1703, 365

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 6812,1460 By Matching Biggest Common Factor Method

Now, list down the factors of 6812

1,2,4,13,26,52,131,262,524,1703,3406,6812

Now, list down the factors of 1460

1,2,4,5,10,20,73,146,292,365,730,1460

Greatest Common Factor

We found the factors 6812,1460 . The biggest common factor number is the GCF number.
So the greatest common factor 6812,1460 is 4.

Lets's calculate LCM of 225,6563

Lowest Common Multiple of 225,6563 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1476675

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/1476675

Therefore, the GCF of Fractions 6812/225,1460/6563 is 4/1476675

Least Common Multiple of 225,6563 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 225,6563 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(225,6563) = 1

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

GCF(225,6563) x common factors =1 x 1 = 1

LCM(225,6563) = ( 225 × 6563 ) / 1

LCM(225,6563) = 1476675 / 1

LCM(225,6563) = 1476675

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 6812/225, 1460/6563

1. What is the HCF of 6812,1460?

The HCF of 6812,1460 is 4

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 6812/225, 1460/6563?

Answer: GCF of Numerators as per given numbers 6812/225, 1460/6563 is

GCF of Numerators i.e. for 6812,1460 is 4

LCM of denominators i.e. for 225,6563 is 1476675.

Thus, GCF of Fractions is 4/1476675.Finally, GCF of Fractions for 6812/225, 1460/6563 is 4/1476675.