How to Find GCF of 64/14, 29/47, 98/58, 31/78?

GCF of 64/14, 29/47, 98/58, 31/78

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 64/14, 29/47, 98/58, 31/78 i.e 1/744198 easily. The following is the detailed procedure to determine the greatest common factor of fractions 64/14, 29/47, 98/58, 31/78.

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 64/14,29/47,98/58,31/78?

Given fractions are 64/14,29/47,98/58,31/78

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 64/14,29/47,98/58,31/78, numerators are 64,29,98,31

Denominators are 14,47,58,78

The GCF of 64,29,98,31 is 1 .

LCM of 14,47,58,78 is 744198.

The greatest common factor of 64/14,29/47,98/58,31/78 = [GCF of 64,29,98,31]/[LCM of 14,47,58,78]= 1/744198

Therefore, the GCF of 64/14,29/47,98/58,31/78 is 1/744198.

Greatest Common Factor of 64,29,98,31

To find the highest common factor of 64,29,98,31, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 29 are 1, 29

The factors of 98 are 1, 2, 7, 14, 49, 98

The factors of 31 are 1, 31

The HCF of 64,29,98,31 is 1.

Lets's calculate GCF of 64,29,98,31

Greatest Common Factor (GCF) of 64,29,98,31 By Common Division

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

Greatest Common Factor of 64,29,98,31 By Matching Biggest Common Factor Method

Now, list down the factors of 64

1,2,4,8,16,32,64

Now, list down the factors of 29

1,29

Now, list down the factors of 98

1,2,7,14,49,98

Now, list down the factors of 31

1,31

Greatest Common Factor

We found the factors 64,29,98,31 . The biggest common factor number is the GCF number.
So the greatest common factor 64,29,98,31 is 1.

Lets's calculate LCM of 14,47,58,78

Lowest Common Multiple of 14,47,58,78 using Common Division

2	14, 47, 58, 78
	7, 47, 29, 39

∴ So the LCM of the given numbers is 2 x 7 x 47 x 29 x 39 = 744198

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/744198

Therefore, the GCF of Fractions 64/14,29/47,98/58,31/78 is 1/744198

Least Common Multiple of 14,47,58,78 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 14,47,58,78 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(14,47,58,78) = 1

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

GCF(14,47,58,78) x common factors =1 x 4 = 4

LCM(14,47,58,78) = ( 14 × 47 × 58 × 78 ) / 4

LCM(14,47,58,78) = 2976792 / 4

LCM(14,47,58,78) = 744198

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 64/14, 29/47, 98/58, 31/78

1. What is the HCF of 64,29,98,31?

The HCF of 64,29,98,31 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 64/14, 29/47, 98/58, 31/78?

Answer: GCF of Numerators as per given numbers 64/14, 29/47, 98/58, 31/78 is

GCF of Numerators i.e. for 64,29,98,31 is 1

LCM of denominators i.e. for 14,47,58,78 is 744198.

Thus, GCF of Fractions is 1/744198.Finally, GCF of Fractions for 64/14, 29/47, 98/58, 31/78 is 1/744198.