How to Find GCF of 280/400, 288/780?

GCF of 280/400, 288/780

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 280/400, 288/780 i.e 8/15600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 280/400, 288/780.

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 280/400,288/780?

Given fractions are 280/400,288/780

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 280/400,288/780, numerators are 280,288

Denominators are 400,780

The GCF of 280,288 is 8 .

LCM of 400,780 is 15600.

The greatest common factor of 280/400,288/780 = [GCF of 280,288]/[LCM of 400,780]= 8/15600

Therefore, the GCF of 280/400,288/780 is 8/15600.

Greatest Common Factor of 280,288

To find the highest common factor of 280,288, we have to find the factors of both numbers and list the highest common factor.

The factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280

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

The HCF of 280,288 is 8.

Lets's calculate GCF of 280,288

Greatest Common Factor (GCF) of 280,288 By Common Division

2	280, 288
2	140, 144
2	70, 72
	35, 36

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 280,288 By Matching Biggest Common Factor Method

Now, list down the factors of 280

1,2,4,5,7,8,10,14,20,28,35,40,56,70,140,280

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

Greatest Common Factor

We found the factors 280,288 . The biggest common factor number is the GCF number.
So the greatest common factor 280,288 is 8.

Lets's calculate LCM of 400,780

Lowest Common Multiple of 400,780 using Common Division

2	400, 780
2	200, 390
5	100, 195
	20, 39

∴ So the LCM of the given numbers is 2 x 2 x 5 x 20 x 39 = 15600

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/15600

Therefore, the GCF of Fractions 280/400,288/780 is 8/15600

Least Common Multiple of 400,780 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 400,780 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(400,780) = 20

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

GCF(400,780) x common factors =20 x 1 = 20

LCM(400,780) = ( 400 × 780 ) / 20

LCM(400,780) = 312000 / 20

LCM(400,780) = 15600

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 280/400, 288/780

1. What is the HCF of 280,288?

The HCF of 280,288 is 8

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 280/400, 288/780?

Answer: GCF of Numerators as per given numbers 280/400, 288/780 is

GCF of Numerators i.e. for 280,288 is 8

LCM of denominators i.e. for 400,780 is 15600.

Thus, GCF of Fractions is 8/15600.Finally, GCF of Fractions for 280/400, 288/780 is 8/15600.