How to Find GCF of 12/28, 90/67, 302/538?

GCF of 12/28, 90/67, 302/538

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 12/28, 90/67, 302/538 i.e 2/504644 easily. The following is the detailed procedure to determine the greatest common factor of fractions 12/28, 90/67, 302/538.

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 12/28,90/67,302/538?

Given fractions are 12/28,90/67,302/538

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 12/28,90/67,302/538, numerators are 12,90,302

Denominators are 28,67,538

The GCF of 12,90,302 is 2 .

LCM of 28,67,538 is 504644.

The greatest common factor of 12/28,90/67,302/538 = [GCF of 12,90,302]/[LCM of 28,67,538]= 2/504644

Therefore, the GCF of 12/28,90/67,302/538 is 2/504644.

Greatest Common Factor of 12,90,302

To find the highest common factor of 12,90,302, we have to find the factors of both numbers and list the highest common factor.

The factors of 12 are 1, 2, 3, 4, 6, 12

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

The factors of 302 are 1, 2, 151, 302

The HCF of 12,90,302 is 2.

Lets's calculate GCF of 12,90,302

Greatest Common Factor (GCF) of 12,90,302 By Common Division

2	12, 90, 302
	6, 45, 151

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

Greatest Common Factor of 12,90,302 By Matching Biggest Common Factor Method

Now, list down the factors of 12

1,2,3,4,6,12

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 302

1,2,151,302

Greatest Common Factor

We found the factors 12,90,302 . The biggest common factor number is the GCF number.
So the greatest common factor 12,90,302 is 2.

Lets's calculate LCM of 28,67,538

Lowest Common Multiple of 28,67,538 using Common Division

2	28, 67, 538
	14, 67, 269

∴ So the LCM of the given numbers is 2 x 14 x 67 x 269 = 504644

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/504644

Therefore, the GCF of Fractions 12/28,90/67,302/538 is 2/504644

Least Common Multiple of 28,67,538 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 28,67,538 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(28,67,538) = 1

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

GCF(28,67,538) x common factors =1 x 2 = 2

LCM(28,67,538) = ( 28 × 67 × 538 ) / 2

LCM(28,67,538) = 1009288 / 2

LCM(28,67,538) = 504644

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 12/28, 90/67, 302/538

1. What is the HCF of 12,90,302?

The HCF of 12,90,302 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 12/28, 90/67, 302/538?

Answer: GCF of Numerators as per given numbers 12/28, 90/67, 302/538 is

GCF of Numerators i.e. for 12,90,302 is 2

LCM of denominators i.e. for 28,67,538 is 504644.

Thus, GCF of Fractions is 2/504644.Finally, GCF of Fractions for 12/28, 90/67, 302/538 is 2/504644.