How to Find GCF of 35/564, 10/760, 238/644?

GCF of 35/564, 10/760, 238/644

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 35/564, 10/760, 238/644 i.e 1/17252760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 35/564, 10/760, 238/644.

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 35/564,10/760,238/644?

Given fractions are 35/564,10/760,238/644

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 35/564,10/760,238/644, numerators are 35,10,238

Denominators are 564,760,644

The GCF of 35,10,238 is 1 .

LCM of 564,760,644 is 17252760.

The greatest common factor of 35/564,10/760,238/644 = [GCF of 35,10,238]/[LCM of 564,760,644]= 1/17252760

Therefore, the GCF of 35/564,10/760,238/644 is 1/17252760.

Greatest Common Factor of 35,10,238

To find the highest common factor of 35,10,238, we have to find the factors of both numbers and list the highest common factor.

The factors of 35 are 1, 5, 7, 35

The factors of 10 are 1, 2, 5, 10

The factors of 238 are 1, 2, 7, 14, 17, 34, 119, 238

The HCF of 35,10,238 is 1.

Lets's calculate GCF of 35,10,238

Greatest Common Factor (GCF) of 35,10,238 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 35,10,238 By Matching Biggest Common Factor Method

Now, list down the factors of 35

1,5,7,35

Now, list down the factors of 10

1,2,5,10

Now, list down the factors of 238

1,2,7,14,17,34,119,238

Greatest Common Factor

We found the factors 35,10,238 . The biggest common factor number is the GCF number.
So the greatest common factor 35,10,238 is 1.

Lets's calculate LCM of 564,760,644

Lowest Common Multiple of 564,760,644 using Common Division

2	564, 760, 644
2	282, 380, 322
	141, 190, 161

∴ So the LCM of the given numbers is 2 x 2 x 141 x 190 x 161 = 17252760

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17252760

Therefore, the GCF of Fractions 35/564,10/760,238/644 is 1/17252760

Least Common Multiple of 564,760,644 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 564,760,644 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(564,760,644) = 4

common factors(in case of two or more numbers have common factors) = 4

GCF(564,760,644) x common factors =4 x 4 = 16

LCM(564,760,644) = ( 564 × 760 × 644 ) / 16

LCM(564,760,644) = 276044160 / 16

LCM(564,760,644) = 17252760

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 35/564, 10/760, 238/644

1. What is the HCF of 35,10,238?

The HCF of 35,10,238 is 1

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 35/564, 10/760, 238/644?

Answer: GCF of Numerators as per given numbers 35/564, 10/760, 238/644 is

GCF of Numerators i.e. for 35,10,238 is 1

LCM of denominators i.e. for 564,760,644 is 17252760.

Thus, GCF of Fractions is 1/17252760.Finally, GCF of Fractions for 35/564, 10/760, 238/644 is 1/17252760.