How to Find GCF of 760/553, 704/538?

GCF of 760/553, 704/538

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 760/553, 704/538 i.e 8/297514 easily. The following is the detailed procedure to determine the greatest common factor of fractions 760/553, 704/538.

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 760/553,704/538?

Given fractions are 760/553,704/538

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 760/553,704/538, numerators are 760,704

Denominators are 553,538

The GCF of 760,704 is 8 .

LCM of 553,538 is 297514.

The greatest common factor of 760/553,704/538 = [GCF of 760,704]/[LCM of 553,538]= 8/297514

Therefore, the GCF of 760/553,704/538 is 8/297514.

Greatest Common Factor of 760,704

To find the highest common factor of 760,704, we have to find the factors of both numbers and list the highest common factor.

The factors of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760

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

The HCF of 760,704 is 8.

Lets's calculate GCF of 760,704

Greatest Common Factor (GCF) of 760,704 By Common Division

2	760, 704
2	380, 352
2	190, 176
	95, 88

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 760,704 By Matching Biggest Common Factor Method

Now, list down the factors of 760

1,2,4,5,8,10,19,20,38,40,76,95,152,190,380,760

Now, list down the factors of 704

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

Greatest Common Factor

We found the factors 760,704 . The biggest common factor number is the GCF number.
So the greatest common factor 760,704 is 8.

Lets's calculate LCM of 553,538

Lowest Common Multiple of 553,538 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 297514

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/297514

Therefore, the GCF of Fractions 760/553,704/538 is 8/297514

Least Common Multiple of 553,538 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 553,538 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(553,538) = 1

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

GCF(553,538) x common factors =1 x 1 = 1

LCM(553,538) = ( 553 × 538 ) / 1

LCM(553,538) = 297514 / 1

LCM(553,538) = 297514

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FAQs on GCF of Fractions of 760/553, 704/538

1. What is the HCF of 760,704?

The HCF of 760,704 is 8

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 760/553, 704/538?

Answer: GCF of Numerators as per given numbers 760/553, 704/538 is

GCF of Numerators i.e. for 760,704 is 8

LCM of denominators i.e. for 553,538 is 297514.

Thus, GCF of Fractions is 8/297514.Finally, GCF of Fractions for 760/553, 704/538 is 8/297514.