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GCF of 180/28, 442/978

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 180/28, 442/978 i.e 2/13692 easily. The following is the detailed procedure to determine the greatest common factor of fractions 180/28, 442/978.

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 180/28,442/978?

Given fractions are 180/28,442/978

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 180/28,442/978, numerators are 180,442

Denominators are 28,978

The GCF of 180,442 is 2 .

LCM of 28,978 is 13692.

The greatest common factor of 180/28,442/978 = [GCF of 180,442]/[LCM of 28,978]= 2/13692

Therefore, the GCF of 180/28,442/978 is 2/13692.

Greatest Common Factor of 180,442

To find the highest common factor of 180,442, we have to find the factors of both numbers and list the highest common factor.

The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

The factors of 442 are 1, 2, 13, 17, 26, 34, 221, 442

The HCF of 180,442 is 2.

Lets's calculate GCF of 180,442

Greatest Common Factor (GCF) of 180,442 By Common Division

2 180, 442
90, 221

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

Greatest Common Factor of 180,442 By Matching Biggest Common Factor Method

Greatest Common Factor of 180,442 By Matching Biggest Common Factor Method

Now, list down the factors of 180

:

1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180

Now, list down the factors of 442

:

1,2,13,17,26,34,221,442

Greatest Common Factor

We found the factors 180,442 . The biggest common factor number is the GCF number.
So the greatest common factor 180,442 is 2.

Lets's calculate LCM of 28,978

Lowest Common Multiple of 28,978 using Common Division

2 28, 978
14, 489

∴ So the LCM of the given numbers is 2 x 14 x 489 = 13692

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/13692

Therefore, the GCF of Fractions 180/28,442/978 is 2/13692

Least Common Multiple of 28,978 with GCF Formula

Least Common Multiple of 28,978 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 28,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(28,978) = 2

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

GCF(28,978) x common factors =2 x 1 = 2

LCM(28,978) = ( 28 × 978 ) / 2

LCM(28,978) = 27384 / 2

LCM(28,978) = 13692


GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 180/28, 442/978

1. What is the HCF of 180,442?

The HCF of 180,442 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 180/28, 442/978?

Answer: GCF of Numerators as per given numbers 180/28, 442/978 is

GCF of Numerators i.e. for 180,442 is 2

LCM of denominators i.e. for 28,978 is 13692.

Thus, GCF of Fractions is 2/13692.Finally, GCF of Fractions for 180/28, 442/978 is 2/13692.