How to Find GCF of 7014/456, 2564/6926?

GCF of 7014/456, 2564/6926

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 7014/456, 2564/6926 i.e 2/1579128 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7014/456, 2564/6926.

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 7014/456,2564/6926?

Given fractions are 7014/456,2564/6926

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 7014/456,2564/6926, numerators are 7014,2564

Denominators are 456,6926

The GCF of 7014,2564 is 2 .

LCM of 456,6926 is 1579128.

The greatest common factor of 7014/456,2564/6926 = [GCF of 7014,2564]/[LCM of 456,6926]= 2/1579128

Therefore, the GCF of 7014/456,2564/6926 is 2/1579128.

Greatest Common Factor of 7014,2564

To find the highest common factor of 7014,2564, we have to find the factors of both numbers and list the highest common factor.

The factors of 7014 are 1, 2, 3, 6, 7, 14, 21, 42, 167, 334, 501, 1002, 1169, 2338, 3507, 7014

The factors of 2564 are 1, 2, 4, 641, 1282, 2564

The HCF of 7014,2564 is 2.

Lets's calculate GCF of 7014,2564

Greatest Common Factor (GCF) of 7014,2564 By Common Division

2	7014, 2564
	3507, 1282

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

Greatest Common Factor of 7014,2564 By Matching Biggest Common Factor Method

Now, list down the factors of 7014

1,2,3,6,7,14,21,42,167,334,501,1002,1169,2338,3507,7014

Now, list down the factors of 2564

1,2,4,641,1282,2564

Greatest Common Factor

We found the factors 7014,2564 . The biggest common factor number is the GCF number.
So the greatest common factor 7014,2564 is 2.

Lets's calculate LCM of 456,6926

Lowest Common Multiple of 456,6926 using Common Division

2	456, 6926
	228, 3463

∴ So the LCM of the given numbers is 2 x 228 x 3463 = 1579128

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1579128

Therefore, the GCF of Fractions 7014/456,2564/6926 is 2/1579128

Least Common Multiple of 456,6926 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 456,6926 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(456,6926) = 2

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

GCF(456,6926) x common factors =2 x 1 = 2

LCM(456,6926) = ( 456 × 6926 ) / 2

LCM(456,6926) = 3158256 / 2

LCM(456,6926) = 1579128

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FAQs on GCF of Fractions of 7014/456, 2564/6926

1. What is the HCF of 7014,2564?

The HCF of 7014,2564 is 2

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 7014/456, 2564/6926?

Answer: GCF of Numerators as per given numbers 7014/456, 2564/6926 is

GCF of Numerators i.e. for 7014,2564 is 2

LCM of denominators i.e. for 456,6926 is 1579128.

Thus, GCF of Fractions is 2/1579128.Finally, GCF of Fractions for 7014/456, 2564/6926 is 2/1579128.