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GCF of 282/78, 723/457

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 282/78, 723/457 i.e 3/35646 easily. The following is the detailed procedure to determine the greatest common factor of fractions 282/78, 723/457.

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 282/78,723/457?

Given fractions are 282/78,723/457

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 282/78,723/457, numerators are 282,723

Denominators are 78,457

The GCF of 282,723 is 3 .

LCM of 78,457 is 35646.

The greatest common factor of 282/78,723/457 = [GCF of 282,723]/[LCM of 78,457]= 3/35646

Therefore, the GCF of 282/78,723/457 is 3/35646.

Greatest Common Factor of 282,723

To find the highest common factor of 282,723, we have to find the factors of both numbers and list the highest common factor.

The factors of 282 are 1, 2, 3, 6, 47, 94, 141, 282

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

The HCF of 282,723 is 3.

Lets's calculate GCF of 282,723

Greatest Common Factor (GCF) of 282,723 By Common Division

3 282, 723
94, 241

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

Greatest Common Factor of 282,723 By Matching Biggest Common Factor Method

Greatest Common Factor of 282,723 By Matching Biggest Common Factor Method

Now, list down the factors of 282

:

1,2,3,6,47,94,141,282

Now, list down the factors of 723

:

1,3,241,723

Greatest Common Factor

We found the factors 282,723 . The biggest common factor number is the GCF number.
So the greatest common factor 282,723 is 3.

Lets's calculate LCM of 78,457

Lowest Common Multiple of 78,457 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 35646

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/35646

Therefore, the GCF of Fractions 282/78,723/457 is 3/35646

Least Common Multiple of 78,457 with GCF Formula

Least Common Multiple of 78,457 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 78,457 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(78,457) = 1

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

GCF(78,457) x common factors =1 x 1 = 1

LCM(78,457) = ( 78 × 457 ) / 1

LCM(78,457) = 35646 / 1

LCM(78,457) = 35646


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FAQs on GCF of Fractions of 282/78, 723/457

1. What is the HCF of 282,723?

The HCF of 282,723 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 282/78, 723/457?

Answer: GCF of Numerators as per given numbers 282/78, 723/457 is

GCF of Numerators i.e. for 282,723 is 3

LCM of denominators i.e. for 78,457 is 35646.

Thus, GCF of Fractions is 3/35646.Finally, GCF of Fractions for 282/78, 723/457 is 3/35646.