How to Find GCF of 323/42, 931/109?

GCF of 323/42, 931/109

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 323/42, 931/109 i.e 19/4578 easily. The following is the detailed procedure to determine the greatest common factor of fractions 323/42, 931/109.

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 323/42,931/109?

Given fractions are 323/42,931/109

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 323/42,931/109, numerators are 323,931

Denominators are 42,109

The GCF of 323,931 is 19 .

LCM of 42,109 is 4578.

The greatest common factor of 323/42,931/109 = [GCF of 323,931]/[LCM of 42,109]= 19/4578

Therefore, the GCF of 323/42,931/109 is 19/4578.

Greatest Common Factor of 323,931

To find the highest common factor of 323,931, we have to find the factors of both numbers and list the highest common factor.

The factors of 323 are 1, 17, 19, 323

The factors of 931 are 1, 7, 19, 49, 133, 931

The HCF of 323,931 is 19.

Lets's calculate GCF of 323,931

Greatest Common Factor (GCF) of 323,931 By Common Division

19	323, 931
	17, 49

∴ So the GCF of the given numbers is 19 = 19

Greatest Common Factor of 323,931 By Matching Biggest Common Factor Method

Now, list down the factors of 323

1,17,19,323

Now, list down the factors of 931

1,7,19,49,133,931

Greatest Common Factor

We found the factors 323,931 . The biggest common factor number is the GCF number.
So the greatest common factor 323,931 is 19.

Lets's calculate LCM of 42,109

Lowest Common Multiple of 42,109 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 4578

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 19/4578

Therefore, the GCF of Fractions 323/42,931/109 is 19/4578

Least Common Multiple of 42,109 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 42,109 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(42,109) = 1

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

GCF(42,109) x common factors =1 x 1 = 1

LCM(42,109) = ( 42 × 109 ) / 1

LCM(42,109) = 4578 / 1

LCM(42,109) = 4578

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 323/42, 931/109

1. What is the HCF of 323,931?

The HCF of 323,931 is 19

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 323/42, 931/109?

Answer: GCF of Numerators as per given numbers 323/42, 931/109 is

GCF of Numerators i.e. for 323,931 is 19

LCM of denominators i.e. for 42,109 is 4578.

Thus, GCF of Fractions is 19/4578.Finally, GCF of Fractions for 323/42, 931/109 is 19/4578.