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GCF of 249/45, 723/184

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 249/45, 723/184 i.e 3/8280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 249/45, 723/184.

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 249/45,723/184?

Given fractions are 249/45,723/184

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 249/45,723/184, numerators are 249,723

Denominators are 45,184

The GCF of 249,723 is 3 .

LCM of 45,184 is 8280.

The greatest common factor of 249/45,723/184 = [GCF of 249,723]/[LCM of 45,184]= 3/8280

Therefore, the GCF of 249/45,723/184 is 3/8280.

Greatest Common Factor of 249,723

To find the highest common factor of 249,723, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 723 are 1, 3, 241, 723

The HCF of 249,723 is 3.

Lets's calculate GCF of 249,723

Greatest Common Factor (GCF) of 249,723 By Common Division

3 249, 723
83, 241

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

Greatest Common Factor of 249,723 By Matching Biggest Common Factor Method

Greatest Common Factor of 249,723 By Matching Biggest Common Factor Method

Now, list down the factors of 249

:

1,3,83,249

Now, list down the factors of 723

:

1,3,241,723

Greatest Common Factor

We found the factors 249,723 . The biggest common factor number is the GCF number.
So the greatest common factor 249,723 is 3.

Lets's calculate LCM of 45,184

Lowest Common Multiple of 45,184 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 8280

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/8280

Therefore, the GCF of Fractions 249/45,723/184 is 3/8280

Least Common Multiple of 45,184 with GCF Formula

Least Common Multiple of 45,184 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 45,184 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(45,184) = 1

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

GCF(45,184) x common factors =1 x 1 = 1

LCM(45,184) = ( 45 × 184 ) / 1

LCM(45,184) = 8280 / 1

LCM(45,184) = 8280


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FAQs on GCF of Fractions of 249/45, 723/184

1. What is the HCF of 249,723?

The HCF of 249,723 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 249/45, 723/184?

Answer: GCF of Numerators as per given numbers 249/45, 723/184 is

GCF of Numerators i.e. for 249,723 is 3

LCM of denominators i.e. for 45,184 is 8280.

Thus, GCF of Fractions is 3/8280.Finally, GCF of Fractions for 249/45, 723/184 is 3/8280.