How to Find GCF of 378/73, 874/8194?

GCF of 378/73, 874/8194

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 378/73, 874/8194 i.e 2/598162 easily. The following is the detailed procedure to determine the greatest common factor of fractions 378/73, 874/8194.

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 378/73,874/8194?

Given fractions are 378/73,874/8194

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 378/73,874/8194, numerators are 378,874

Denominators are 73,8194

The GCF of 378,874 is 2 .

LCM of 73,8194 is 598162.

The greatest common factor of 378/73,874/8194 = [GCF of 378,874]/[LCM of 73,8194]= 2/598162

Therefore, the GCF of 378/73,874/8194 is 2/598162.

Greatest Common Factor of 378,874

To find the highest common factor of 378,874, we have to find the factors of both numbers and list the highest common factor.

The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378

The factors of 874 are 1, 2, 19, 23, 38, 46, 437, 874

The HCF of 378,874 is 2.

Lets's calculate GCF of 378,874

Greatest Common Factor (GCF) of 378,874 By Common Division

2	378, 874
	189, 437

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

Greatest Common Factor of 378,874 By Matching Biggest Common Factor Method

Now, list down the factors of 378

1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378

Now, list down the factors of 874

1,2,19,23,38,46,437,874

Greatest Common Factor

We found the factors 378,874 . The biggest common factor number is the GCF number.
So the greatest common factor 378,874 is 2.

Lets's calculate LCM of 73,8194

Lowest Common Multiple of 73,8194 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 598162

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/598162

Therefore, the GCF of Fractions 378/73,874/8194 is 2/598162

Least Common Multiple of 73,8194 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 73,8194 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(73,8194) = 1

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

GCF(73,8194) x common factors =1 x 1 = 1

LCM(73,8194) = ( 73 × 8194 ) / 1

LCM(73,8194) = 598162 / 1

LCM(73,8194) = 598162

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 378/73, 874/8194

1. What is the HCF of 378,874?

The HCF of 378,874 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 378/73, 874/8194?

Answer: GCF of Numerators as per given numbers 378/73, 874/8194 is

GCF of Numerators i.e. for 378,874 is 2

LCM of denominators i.e. for 73,8194 is 598162.

Thus, GCF of Fractions is 2/598162.Finally, GCF of Fractions for 378/73, 874/8194 is 2/598162.