How to Find GCF of 288/277, 768/823?

GCF of 288/277, 768/823

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 288/277, 768/823 i.e 96/227971 easily. The following is the detailed procedure to determine the greatest common factor of fractions 288/277, 768/823.

Enter two or more fractions separated by "commas"

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

What is the GCF of 288/277,768/823?

Given fractions are 288/277,768/823

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 288/277,768/823, numerators are 288,768

Denominators are 277,823

The GCF of 288,768 is 96 .

LCM of 277,823 is 227971.

The greatest common factor of 288/277,768/823 = [GCF of 288,768]/[LCM of 277,823]= 96/227971

Therefore, the GCF of 288/277,768/823 is 96/227971.

Greatest Common Factor of 288,768

To find the highest common factor of 288,768, we have to find the factors of both numbers and list the highest common factor.

The factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288

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 288,768 is 96.

Lets's calculate GCF of 288,768

Greatest Common Factor (GCF) of 288,768 By Common Division

2	288, 768
2	144, 384
2	72, 192
2	36, 96
2	18, 48
3	9, 24
	3, 8

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 x 3 = 96

Greatest Common Factor of 288,768 By Matching Biggest Common Factor Method

Now, list down the factors of 288

1,2,3,4,6,8,9,12,16,18,24,32,36,48,72,96,144,288

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 288,768 . The biggest common factor number is the GCF number.
So the greatest common factor 288,768 is 96.

Lets's calculate LCM of 277,823

Lowest Common Multiple of 277,823 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 227971

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 96/227971

Therefore, the GCF of Fractions 288/277,768/823 is 96/227971

Least Common Multiple of 277,823 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 277,823 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(277,823) = 1

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

GCF(277,823) x common factors =1 x 1 = 1

LCM(277,823) = ( 277 × 823 ) / 1

LCM(277,823) = 227971 / 1

LCM(277,823) = 227971

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FAQs on GCF of Fractions of 288/277, 768/823

1. What is the HCF of 288,768?

The HCF of 288,768 is 96

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 288/277, 768/823?

Answer: GCF of Numerators as per given numbers 288/277, 768/823 is

GCF of Numerators i.e. for 288,768 is 96

LCM of denominators i.e. for 277,823 is 227971.

Thus, GCF of Fractions is 96/227971.Finally, GCF of Fractions for 288/277, 768/823 is 96/227971.