How to Find GCF of 42/294, 13/867, 514/119?

GCF of 42/294, 13/867, 514/119

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 42/294, 13/867, 514/119 i.e 1/84966 easily. The following is the detailed procedure to determine the greatest common factor of fractions 42/294, 13/867, 514/119.

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 42/294,13/867,514/119?

Given fractions are 42/294,13/867,514/119

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 42/294,13/867,514/119, numerators are 42,13,514

Denominators are 294,867,119

The GCF of 42,13,514 is 1 .

LCM of 294,867,119 is 84966.

The greatest common factor of 42/294,13/867,514/119 = [GCF of 42,13,514]/[LCM of 294,867,119]= 1/84966

Therefore, the GCF of 42/294,13/867,514/119 is 1/84966.

Greatest Common Factor of 42,13,514

To find the highest common factor of 42,13,514, we have to find the factors of both numbers and list the highest common factor.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42

The factors of 13 are 1, 13

The factors of 514 are 1, 2, 257, 514

The HCF of 42,13,514 is 1.

Lets's calculate GCF of 42,13,514

Greatest Common Factor (GCF) of 42,13,514 By Common Division

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

Greatest Common Factor of 42,13,514 By Matching Biggest Common Factor Method

Now, list down the factors of 42

1,2,3,6,7,14,21,42

Now, list down the factors of 13

1,13

Now, list down the factors of 514

1,2,257,514

Greatest Common Factor

We found the factors 42,13,514 . The biggest common factor number is the GCF number.
So the greatest common factor 42,13,514 is 1.

Lets's calculate LCM of 294,867,119

Lowest Common Multiple of 294,867,119 using Common Division

3	294, 867, 119
7	98, 289, 119
17	14, 289, 17
	14, 1, 17

∴ So the LCM of the given numbers is 3 x 7 x 17 x 14 x 1 x 17 = 84966

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/84966

Therefore, the GCF of Fractions 42/294,13/867,514/119 is 1/84966

Least Common Multiple of 294,867,119 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 294,867,119 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(294,867,119) = 1

common factors(in case of two or more numbers have common factors) = 357

GCF(294,867,119) x common factors =1 x 357 = 357

LCM(294,867,119) = ( 294 × 867 × 119 ) / 357

LCM(294,867,119) = 30332862 / 357

LCM(294,867,119) = 84966

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 42/294, 13/867, 514/119

1. What is the HCF of 42,13,514?

The HCF of 42,13,514 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 42/294, 13/867, 514/119?

Answer: GCF of Numerators as per given numbers 42/294, 13/867, 514/119 is

GCF of Numerators i.e. for 42,13,514 is 1

LCM of denominators i.e. for 294,867,119 is 84966.

Thus, GCF of Fractions is 1/84966.Finally, GCF of Fractions for 42/294, 13/867, 514/119 is 1/84966.