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GCF of 628/204, 768/225

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 628/204, 768/225 i.e 4/15300 easily. The following is the detailed procedure to determine the greatest common factor of fractions 628/204, 768/225.

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 628/204,768/225?

Given fractions are 628/204,768/225

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 628/204,768/225, numerators are 628,768

Denominators are 204,225

The GCF of 628,768 is 4 .

LCM of 204,225 is 15300.

The greatest common factor of 628/204,768/225 = [GCF of 628,768]/[LCM of 204,225]= 4/15300

Therefore, the GCF of 628/204,768/225 is 4/15300.

Greatest Common Factor of 628,768

To find the highest common factor of 628,768, we have to find the factors of both numbers and list the highest common factor.

The factors of 628 are 1, 2, 4, 157, 314, 628

The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768

The HCF of 628,768 is 4.

Lets's calculate GCF of 628,768

Greatest Common Factor (GCF) of 628,768 By Common Division

2 628, 768
2 314, 384
157, 192

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 628,768 By Matching Biggest Common Factor Method

Greatest Common Factor of 628,768 By Matching Biggest Common Factor Method

Now, list down the factors of 628

:

1,2,4,157,314,628

Now, list down the factors of 768

:

1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768

Greatest Common Factor

We found the factors 628,768 . The biggest common factor number is the GCF number.
So the greatest common factor 628,768 is 4.

Lets's calculate LCM of 204,225

Lowest Common Multiple of 204,225 using Common Division

3 204, 225
68, 75

∴ So the LCM of the given numbers is 3 x 68 x 75 = 15300

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/15300

Therefore, the GCF of Fractions 628/204,768/225 is 4/15300

Least Common Multiple of 204,225 with GCF Formula

Least Common Multiple of 204,225 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 204,225 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(204,225) = 3

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

GCF(204,225) x common factors =3 x 1 = 3

LCM(204,225) = ( 204 × 225 ) / 3

LCM(204,225) = 45900 / 3

LCM(204,225) = 15300


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FAQs on GCF of Fractions of 628/204, 768/225

1. What is the HCF of 628,768?

The HCF of 628,768 is 4

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 628/204, 768/225?

Answer: GCF of Numerators as per given numbers 628/204, 768/225 is

GCF of Numerators i.e. for 628,768 is 4

LCM of denominators i.e. for 204,225 is 15300.

Thus, GCF of Fractions is 4/15300.Finally, GCF of Fractions for 628/204, 768/225 is 4/15300.