How to Find GCF of 49/64, 53/39, 114/142?

GCF of 49/64, 53/39, 114/142

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 49/64, 53/39, 114/142 i.e 1/177216 easily. The following is the detailed procedure to determine the greatest common factor of fractions 49/64, 53/39, 114/142.

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 49/64,53/39,114/142?

Given fractions are 49/64,53/39,114/142

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 49/64,53/39,114/142, numerators are 49,53,114

Denominators are 64,39,142

The GCF of 49,53,114 is 1 .

LCM of 64,39,142 is 177216.

The greatest common factor of 49/64,53/39,114/142 = [GCF of 49,53,114]/[LCM of 64,39,142]= 1/177216

Therefore, the GCF of 49/64,53/39,114/142 is 1/177216.

Greatest Common Factor of 49,53,114

To find the highest common factor of 49,53,114, we have to find the factors of both numbers and list the highest common factor.

The factors of 49 are 1, 7, 49

The factors of 53 are 1, 53

The factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114

The HCF of 49,53,114 is 1.

Lets's calculate GCF of 49,53,114

Greatest Common Factor (GCF) of 49,53,114 By Common Division

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

Greatest Common Factor of 49,53,114 By Matching Biggest Common Factor Method

Now, list down the factors of 49

1,7,49

Now, list down the factors of 53

1,53

Now, list down the factors of 114

1,2,3,6,19,38,57,114

Greatest Common Factor

We found the factors 49,53,114 . The biggest common factor number is the GCF number.
So the greatest common factor 49,53,114 is 1.

Lets's calculate LCM of 64,39,142

Lowest Common Multiple of 64,39,142 using Common Division

2	64, 39, 142
	32, 39, 71

∴ So the LCM of the given numbers is 2 x 32 x 39 x 71 = 177216

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/177216

Therefore, the GCF of Fractions 49/64,53/39,114/142 is 1/177216

Least Common Multiple of 64,39,142 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 64,39,142 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(64,39,142) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(64,39,142) x common factors =1 x 2 = 2

LCM(64,39,142) = ( 64 × 39 × 142 ) / 2

LCM(64,39,142) = 354432 / 2

LCM(64,39,142) = 177216

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FAQs on GCF of Fractions of 49/64, 53/39, 114/142

1. What is the HCF of 49,53,114?

The HCF of 49,53,114 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 49/64, 53/39, 114/142?

Answer: GCF of Numerators as per given numbers 49/64, 53/39, 114/142 is

GCF of Numerators i.e. for 49,53,114 is 1

LCM of denominators i.e. for 64,39,142 is 177216.

Thus, GCF of Fractions is 1/177216.Finally, GCF of Fractions for 49/64, 53/39, 114/142 is 1/177216.