How to Find GCF of 52/74, 90/13, 14/58?

GCF of 52/74, 90/13, 14/58

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 52/74, 90/13, 14/58 i.e 2/27898 easily. The following is the detailed procedure to determine the greatest common factor of fractions 52/74, 90/13, 14/58.

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 52/74,90/13,14/58?

Given fractions are 52/74,90/13,14/58

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 52/74,90/13,14/58, numerators are 52,90,14

Denominators are 74,13,58

The GCF of 52,90,14 is 2 .

LCM of 74,13,58 is 27898.

The greatest common factor of 52/74,90/13,14/58 = [GCF of 52,90,14]/[LCM of 74,13,58]= 2/27898

Therefore, the GCF of 52/74,90/13,14/58 is 2/27898.

Greatest Common Factor of 52,90,14

To find the highest common factor of 52,90,14, we have to find the factors of both numbers and list the highest common factor.

The factors of 52 are 1, 2, 4, 13, 26, 52

The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

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

The HCF of 52,90,14 is 2.

Lets's calculate GCF of 52,90,14

Greatest Common Factor (GCF) of 52,90,14 By Common Division

2	52, 90, 14
	26, 45, 7

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

Greatest Common Factor of 52,90,14 By Matching Biggest Common Factor Method

Now, list down the factors of 52

1,2,4,13,26,52

Now, list down the factors of 90

1,2,3,5,6,9,10,15,18,30,45,90

Now, list down the factors of 14

1,2,7,14

Greatest Common Factor

We found the factors 52,90,14 . The biggest common factor number is the GCF number.
So the greatest common factor 52,90,14 is 2.

Lets's calculate LCM of 74,13,58

Lowest Common Multiple of 74,13,58 using Common Division

2	74, 13, 58
	37, 13, 29

∴ So the LCM of the given numbers is 2 x 37 x 13 x 29 = 27898

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/27898

Therefore, the GCF of Fractions 52/74,90/13,14/58 is 2/27898

Least Common Multiple of 74,13,58 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 74,13,58 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(74,13,58) = 1

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

GCF(74,13,58) x common factors =1 x 2 = 2

LCM(74,13,58) = ( 74 × 13 × 58 ) / 2

LCM(74,13,58) = 55796 / 2

LCM(74,13,58) = 27898

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FAQs on GCF of Fractions of 52/74, 90/13, 14/58

1. What is the HCF of 52,90,14?

The HCF of 52,90,14 is 2

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 52/74, 90/13, 14/58?

Answer: GCF of Numerators as per given numbers 52/74, 90/13, 14/58 is

GCF of Numerators i.e. for 52,90,14 is 2

LCM of denominators i.e. for 74,13,58 is 27898.

Thus, GCF of Fractions is 2/27898.Finally, GCF of Fractions for 52/74, 90/13, 14/58 is 2/27898.