How to Find GCF of 14/228, 18/499, 194/654?

GCF of 14/228, 18/499, 194/654

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 14/228, 18/499, 194/654 i.e 2/12401148 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/228, 18/499, 194/654.

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 14/228,18/499,194/654?

Given fractions are 14/228,18/499,194/654

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 14/228,18/499,194/654, numerators are 14,18,194

Denominators are 228,499,654

The GCF of 14,18,194 is 2 .

LCM of 228,499,654 is 12401148.

The greatest common factor of 14/228,18/499,194/654 = [GCF of 14,18,194]/[LCM of 228,499,654]= 2/12401148

Therefore, the GCF of 14/228,18/499,194/654 is 2/12401148.

Greatest Common Factor of 14,18,194

To find the highest common factor of 14,18,194, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 18 are 1, 2, 3, 6, 9, 18

The factors of 194 are 1, 2, 97, 194

The HCF of 14,18,194 is 2.

Lets's calculate GCF of 14,18,194

Greatest Common Factor (GCF) of 14,18,194 By Common Division

2	14, 18, 194
	7, 9, 97

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

Greatest Common Factor of 14,18,194 By Matching Biggest Common Factor Method

Now, list down the factors of 14

1,2,7,14

Now, list down the factors of 18

1,2,3,6,9,18

Now, list down the factors of 194

1,2,97,194

Greatest Common Factor

We found the factors 14,18,194 . The biggest common factor number is the GCF number.
So the greatest common factor 14,18,194 is 2.

Lets's calculate LCM of 228,499,654

Lowest Common Multiple of 228,499,654 using Common Division

2	228, 499, 654
3	114, 499, 327
	38, 499, 109

∴ So the LCM of the given numbers is 2 x 3 x 38 x 499 x 109 = 12401148

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/12401148

Therefore, the GCF of Fractions 14/228,18/499,194/654 is 2/12401148

Least Common Multiple of 228,499,654 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 228,499,654 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(228,499,654) = 1

common factors(in case of two or more numbers have common factors) = 6

GCF(228,499,654) x common factors =1 x 6 = 6

LCM(228,499,654) = ( 228 × 499 × 654 ) / 6

LCM(228,499,654) = 74406888 / 6

LCM(228,499,654) = 12401148

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 14/228, 18/499, 194/654

1. What is the HCF of 14,18,194?

The HCF of 14,18,194 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 14/228, 18/499, 194/654?

Answer: GCF of Numerators as per given numbers 14/228, 18/499, 194/654 is

GCF of Numerators i.e. for 14,18,194 is 2

LCM of denominators i.e. for 228,499,654 is 12401148.

Thus, GCF of Fractions is 2/12401148.Finally, GCF of Fractions for 14/228, 18/499, 194/654 is 2/12401148.