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GCF of 375/14, 249/406

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 375/14, 249/406 i.e 3/406 easily. The following is the detailed procedure to determine the greatest common factor of fractions 375/14, 249/406.

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 375/14,249/406?

Given fractions are 375/14,249/406

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 375/14,249/406, numerators are 375,249

Denominators are 14,406

The GCF of 375,249 is 3 .

LCM of 14,406 is 406.

The greatest common factor of 375/14,249/406 = [GCF of 375,249]/[LCM of 14,406]= 3/406

Therefore, the GCF of 375/14,249/406 is 3/406.

Greatest Common Factor of 375,249

To find the highest common factor of 375,249, we have to find the factors of both numbers and list the highest common factor.

The factors of 375 are 1, 3, 5, 15, 25, 75, 125, 375

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

The HCF of 375,249 is 3.

Lets's calculate GCF of 375,249

Greatest Common Factor (GCF) of 375,249 By Common Division

3 375, 249
125, 83

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

Greatest Common Factor of 375,249 By Matching Biggest Common Factor Method

Greatest Common Factor of 375,249 By Matching Biggest Common Factor Method

Now, list down the factors of 375

:

1,3,5,15,25,75,125,375

Now, list down the factors of 249

:

1,3,83,249

Greatest Common Factor

We found the factors 375,249 . The biggest common factor number is the GCF number.
So the greatest common factor 375,249 is 3.

Lets's calculate LCM of 14,406

Lowest Common Multiple of 14,406 using Common Division

2 14, 406
7 7, 203
1, 29

∴ So the LCM of the given numbers is 2 x 7 x 1 x 29 = 406

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/406

Therefore, the GCF of Fractions 375/14,249/406 is 3/406

Least Common Multiple of 14,406 with GCF Formula

Least Common Multiple of 14,406 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 14,406 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(14,406) = 14

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

GCF(14,406) x common factors =14 x 1 = 14

LCM(14,406) = ( 14 × 406 ) / 14

LCM(14,406) = 5684 / 14

LCM(14,406) = 406


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FAQs on GCF of Fractions of 375/14, 249/406

1. What is the HCF of 375,249?

The HCF of 375,249 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 375/14, 249/406?

Answer: GCF of Numerators as per given numbers 375/14, 249/406 is

GCF of Numerators i.e. for 375,249 is 3

LCM of denominators i.e. for 14,406 is 406.

Thus, GCF of Fractions is 3/406.Finally, GCF of Fractions for 375/14, 249/406 is 3/406.