How to Find GCF of 704/562, 512/313?

GCF of 704/562, 512/313

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 704/562, 512/313 i.e 64/175906 easily. The following is the detailed procedure to determine the greatest common factor of fractions 704/562, 512/313.

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 704/562,512/313?

Given fractions are 704/562,512/313

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 704/562,512/313, numerators are 704,512

Denominators are 562,313

The GCF of 704,512 is 64 .

LCM of 562,313 is 175906.

The greatest common factor of 704/562,512/313 = [GCF of 704,512]/[LCM of 562,313]= 64/175906

Therefore, the GCF of 704/562,512/313 is 64/175906.

Greatest Common Factor of 704,512

To find the highest common factor of 704,512, we have to find the factors of both numbers and list the highest common factor.

The factors of 704 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352, 704

The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512

The HCF of 704,512 is 64.

Lets's calculate GCF of 704,512

Greatest Common Factor (GCF) of 704,512 By Common Division

2	704, 512
2	352, 256
2	176, 128
2	88, 64
2	44, 32
2	22, 16
	11, 8

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 = 64

Greatest Common Factor of 704,512 By Matching Biggest Common Factor Method

Now, list down the factors of 704

1,2,4,8,11,16,22,32,44,64,88,176,352,704

Now, list down the factors of 512

1,2,4,8,16,32,64,128,256,512

Greatest Common Factor

We found the factors 704,512 . The biggest common factor number is the GCF number.
So the greatest common factor 704,512 is 64.

Lets's calculate LCM of 562,313

Lowest Common Multiple of 562,313 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 175906

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 64/175906

Therefore, the GCF of Fractions 704/562,512/313 is 64/175906

Least Common Multiple of 562,313 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 562,313 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(562,313) = 1

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

GCF(562,313) x common factors =1 x 1 = 1

LCM(562,313) = ( 562 × 313 ) / 1

LCM(562,313) = 175906 / 1

LCM(562,313) = 175906

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FAQs on GCF of Fractions of 704/562, 512/313

1. What is the HCF of 704,512?

The HCF of 704,512 is 64

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 704/562, 512/313?

Answer: GCF of Numerators as per given numbers 704/562, 512/313 is

GCF of Numerators i.e. for 704,512 is 64

LCM of denominators i.e. for 562,313 is 175906.

Thus, GCF of Fractions is 64/175906.Finally, GCF of Fractions for 704/562, 512/313 is 64/175906.