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GCF of 20/149, 78/924

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 20/149, 78/924 i.e 2/137676 easily. The following is the detailed procedure to determine the greatest common factor of fractions 20/149, 78/924.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 20/149,78/924?

Given fractions are 20/149,78/924

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 20/149,78/924, numerators are 20,78

Denominators are 149,924

The GCF of 20,78 is 2 .

LCM of 149,924 is 137676.

The greatest common factor of 20/149,78/924 = [GCF of 20,78]/[LCM of 149,924]= 2/137676

Therefore, the GCF of 20/149,78/924 is 2/137676.

Greatest Common Factor of 20,78

To find the highest common factor of 20,78, we have to find the factors of both numbers and list the highest common factor.

The factors of 20 are 1, 2, 4, 5, 10, 20

The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78

The HCF of 20,78 is 2.

Lets's calculate GCF of 20,78

Greatest Common Factor (GCF) of 20,78 By Common Division

2 20, 78
10, 39

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

Greatest Common Factor of 20,78 By Matching Biggest Common Factor Method

Greatest Common Factor of 20,78 By Matching Biggest Common Factor Method

Now, list down the factors of 20

:

1,2,4,5,10,20

Now, list down the factors of 78

:

1,2,3,6,13,26,39,78

Greatest Common Factor

We found the factors 20,78 . The biggest common factor number is the GCF number.
So the greatest common factor 20,78 is 2.

Lets's calculate LCM of 149,924

Lowest Common Multiple of 149,924 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 137676

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/137676

Therefore, the GCF of Fractions 20/149,78/924 is 2/137676

Least Common Multiple of 149,924 with GCF Formula

Least Common Multiple of 149,924 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 149,924 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(149,924) = 1

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

GCF(149,924) x common factors =1 x 1 = 1

LCM(149,924) = ( 149 × 924 ) / 1

LCM(149,924) = 137676 / 1

LCM(149,924) = 137676


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FAQs on GCF of Fractions of 20/149, 78/924

1. What is the HCF of 20,78?

The HCF of 20,78 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 20/149, 78/924?

Answer: GCF of Numerators as per given numbers 20/149, 78/924 is

GCF of Numerators i.e. for 20,78 is 2

LCM of denominators i.e. for 149,924 is 137676.

Thus, GCF of Fractions is 2/137676.Finally, GCF of Fractions for 20/149, 78/924 is 2/137676.