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GCF of 21/78, 15/21, 249/46

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 21/78, 15/21, 249/46 i.e 3/12558 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/78, 15/21, 249/46.

Enter two or more fractions separated by "commas"

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

GCF of:

What is the GCF of 21/78,15/21,249/46?

Given fractions are 21/78,15/21,249/46

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 21/78,15/21,249/46, numerators are 21,15,249

Denominators are 78,21,46

The GCF of 21,15,249 is 3 .

LCM of 78,21,46 is 12558.

The greatest common factor of 21/78,15/21,249/46 = [GCF of 21,15,249]/[LCM of 78,21,46]= 3/12558

Therefore, the GCF of 21/78,15/21,249/46 is 3/12558.

Greatest Common Factor of 21,15,249

To find the highest common factor of 21,15,249, we have to find the factors of both numbers and list the highest common factor.

The factors of 21 are 1, 3, 7, 21

The factors of 15 are 1, 3, 5, 15

The factors of 249 are 1, 3, 83, 249

The HCF of 21,15,249 is 3.

Lets's calculate GCF of 21,15,249

Greatest Common Factor (GCF) of 21,15,249 By Common Division

3 21, 15, 249
7, 5, 83

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 21,15,249 By Matching Biggest Common Factor Method

Greatest Common Factor of 21,15,249 By Matching Biggest Common Factor Method

Now, list down the factors of 21

:

1,3,7,21

Now, list down the factors of 15

:

1,3,5,15

Now, list down the factors of 249

:

1,3,83,249

Greatest Common Factor

We found the factors 21,15,249 . The biggest common factor number is the GCF number.
So the greatest common factor 21,15,249 is 3.


Lets's calculate LCM of 78,21,46

Lowest Common Multiple of 78,21,46 using Common Division

2 78, 21, 46
3 39, 21, 23
13, 7, 23

∴ So the LCM of the given numbers is 2 x 3 x 13 x 7 x 23 = 12558

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/12558

Therefore, the GCF of Fractions 21/78,15/21,249/46 is 3/12558

Least Common Multiple of 78,21,46 with GCF Formula

Least Common Multiple of 78,21,46 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 78,21,46 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(78,21,46) = 1

common factors(in case of two or more numbers have common factors) = 6

GCF(78,21,46) x common factors =1 x 6 = 6

LCM(78,21,46) = ( 78 × 21 × 46 ) / 6

LCM(78,21,46) = 75348 / 6

LCM(78,21,46) = 12558


GCF of Fractions Calculation Examples

FAQs on GCF of Fractions of 21/78, 15/21, 249/46

1. What is the HCF of 21,15,249?

The HCF of 21,15,249 is 3

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 21/78, 15/21, 249/46?

Answer: GCF of Numerators as per given numbers 21/78, 15/21, 249/46 is

GCF of Numerators i.e. for 21,15,249 is 3

LCM of denominators i.e. for 78,21,46 is 12558.

Thus, GCF of Fractions is 3/12558.Finally, GCF of Fractions for 21/78, 15/21, 249/46 is 3/12558.