How to Find GCF of 13/238, 13/154, 309/210?

GCF of 13/238, 13/154, 309/210

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 13/238, 13/154, 309/210 i.e 1/39270 easily. The following is the detailed procedure to determine the greatest common factor of fractions 13/238, 13/154, 309/210.

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 13/238,13/154,309/210?

Given fractions are 13/238,13/154,309/210

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 13/238,13/154,309/210, numerators are 13,13,309

Denominators are 238,154,210

The GCF of 13,13,309 is 1 .

LCM of 238,154,210 is 39270.

The greatest common factor of 13/238,13/154,309/210 = [GCF of 13,13,309]/[LCM of 238,154,210]= 1/39270

Therefore, the GCF of 13/238,13/154,309/210 is 1/39270.

Greatest Common Factor of 13,13,309

To find the highest common factor of 13,13,309, we have to find the factors of both numbers and list the highest common factor.

The factors of 13 are 1, 13

The factors of 309 are 1, 3, 103, 309

The HCF of 13,13,309 is 1.

Lets's calculate GCF of 13,13,309

Greatest Common Factor (GCF) of 13,13,309 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 13,13,309 By Matching Biggest Common Factor Method

Now, list down the factors of 13

1,13

Now, list down the factors of 13

1,13

Now, list down the factors of 309

1,3,103,309

Greatest Common Factor

We found the factors 13,13,309 . The biggest common factor number is the GCF number.
So the greatest common factor 13,13,309 is 1.

Lets's calculate LCM of 238,154,210

Lowest Common Multiple of 238,154,210 using Common Division

2	238, 154, 210
7	119, 77, 105
	17, 11, 15

∴ So the LCM of the given numbers is 2 x 7 x 17 x 11 x 15 = 39270

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/39270

Therefore, the GCF of Fractions 13/238,13/154,309/210 is 1/39270

Least Common Multiple of 238,154,210 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 238,154,210 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(238,154,210) = 14

common factors(in case of two or more numbers have common factors) = 14

GCF(238,154,210) x common factors =14 x 14 = 196

LCM(238,154,210) = ( 238 × 154 × 210 ) / 196

LCM(238,154,210) = 7696920 / 196

LCM(238,154,210) = 39270

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 13/238, 13/154, 309/210

1. What is the HCF of 13,13,309?

The HCF of 13,13,309 is 1

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 13/238, 13/154, 309/210?

Answer: GCF of Numerators as per given numbers 13/238, 13/154, 309/210 is

GCF of Numerators i.e. for 13,13,309 is 1

LCM of denominators i.e. for 238,154,210 is 39270.

Thus, GCF of Fractions is 1/39270.Finally, GCF of Fractions for 13/238, 13/154, 309/210 is 1/39270.