Greatest Common Factor of 34/24, 14/48, 32/24, 21/15

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 34/24, 14/48, 32/24, 21/15

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

Greatest Common Factor of 34/24,14/48,32/24,21/15

Given fractions are 34/24,14/48,32/24,21/15

Formula to find GCF of Fractions is

GCF = GCF of Numerators/LCM of Denominators

As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators

In the given fractions GCF of Numerators means GCF of 34,14,32,21

Greatest Common Factor of Numerators i.e. GCF of 34,14,32,21 is 1 .

LCM of Denominators means LCM of 24,48,24,15 as per the given fractions.

LCM of 24,48,24,15 is 240 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 34,14,32,21

GCF of Fractions 34/24,14/48,32/24,21/15 is 1/240

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

Greatest Common Factor of 34,14,32,21 By Matching Biggest Common Factor Method

Greatest Common Factor of 34,14,32,21 By Matching Biggest Common Factor Method

Factors of 34

List of positive integer factors of 34 that divides 34 without a remainder.

1,2,17,34

Factors of 14

List of positive integer factors of 14 that divides 14 without a remainder.

1,2,7,14

Factors of 32

List of positive integer factors of 32 that divides 32 without a remainder.

1,2,4,8,16,32

Factors of 21

List of positive integer factors of 21 that divides 21 without a remainder.

1,3,7,21

Greatest Common Factor

We found the factors 34,14,32,21 . The biggest common factor number is the GCF number.
So the greatest common factor 34,14,32,21 is 1.

Lets's calculate LCM of 24,48,24,15

2 24, 48, 24, 15
2 12, 24, 12, 15
2 6, 6, 12, 15
3 3, 3, 6, 15
1, 1, 2, 5

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 1 x 1 x 2 x 5 = 240

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/240

Therefore, the GCF of Fractions 34/24,14/48,32/24,21/15 is 1/240

Least Common Multiple of 24,48,24,15 with GCF Formula

Least Common Multiple of 24,48,24,15 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 24,48,24,15 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(24,48,24,15) = 3

common factors(in case of two or more numbers have common factors) = 576

GCF(24,48,24,15) x common factors =3 x 576 = 1728

LCM(24,48,24,15) = ( 24 × 48 × 24 × 15 ) / 1728

LCM(24,48,24,15) = 414720 / 1728

LCM(24,48,24,15) = 240


GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

Frequently Asked Questions on Fractional GCF of 34/24, 14/48, 32/24, 21/15

1. 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.

2. What is the GCF of Fractions for 34/24, 14/48, 32/24, 21/15?

Answer: GCF of Numerators as per given numbers 34/24, 14/48, 32/24, 21/15 is

GCF of Numerators i.e. for 34,14,32,21 is 1

LCM of denominators i.e. for 24,48,24,15 is 240.

Thus, GCF of Fractions is 1/240.Finally, GCF of Fractions for 34/24, 14/48, 32/24, 21/15 is 1/240.