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GCF of 422/33, 138/5574

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 422/33, 138/5574 i.e 2/61314 easily. The following is the detailed procedure to determine the greatest common factor of fractions 422/33, 138/5574.

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 422/33,138/5574?

Given fractions are 422/33,138/5574

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 422/33,138/5574, numerators are 422,138

Denominators are 33,5574

The GCF of 422,138 is 2 .

LCM of 33,5574 is 61314.

The greatest common factor of 422/33,138/5574 = [GCF of 422,138]/[LCM of 33,5574]= 2/61314

Therefore, the GCF of 422/33,138/5574 is 2/61314.

Greatest Common Factor of 422,138

To find the highest common factor of 422,138, we have to find the factors of both numbers and list the highest common factor.

The factors of 422 are 1, 2, 211, 422

The factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138

The HCF of 422,138 is 2.

Lets's calculate GCF of 422,138

Greatest Common Factor (GCF) of 422,138 By Common Division

2 422, 138
211, 69

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

Greatest Common Factor of 422,138 By Matching Biggest Common Factor Method

Greatest Common Factor of 422,138 By Matching Biggest Common Factor Method

Now, list down the factors of 422

:

1,2,211,422

Now, list down the factors of 138

:

1,2,3,6,23,46,69,138

Greatest Common Factor

We found the factors 422,138 . The biggest common factor number is the GCF number.
So the greatest common factor 422,138 is 2.


Lets's calculate LCM of 33,5574

Lowest Common Multiple of 33,5574 using Common Division

3 33, 5574
11, 1858

∴ So the LCM of the given numbers is 3 x 11 x 1858 = 61314

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/61314

Therefore, the GCF of Fractions 422/33,138/5574 is 2/61314

Least Common Multiple of 33,5574 with GCF Formula

Least Common Multiple of 33,5574 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 33,5574 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(33,5574) = 3

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

GCF(33,5574) x common factors =3 x 1 = 3

LCM(33,5574) = ( 33 × 5574 ) / 3

LCM(33,5574) = 183942 / 3

LCM(33,5574) = 61314


GCF of Fractions Calculation Examples

FAQs on GCF of Fractions of 422/33, 138/5574

1. What is the HCF of 422,138?

The HCF of 422,138 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 422/33, 138/5574?

Answer: GCF of Numerators as per given numbers 422/33, 138/5574 is

GCF of Numerators i.e. for 422,138 is 2

LCM of denominators i.e. for 33,5574 is 61314.

Thus, GCF of Fractions is 2/61314.Finally, GCF of Fractions for 422/33, 138/5574 is 2/61314.