How to Find GCF of 320/38, 280/787?

GCF of 320/38, 280/787

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 320/38, 280/787 i.e 40/29906 easily. The following is the detailed procedure to determine the greatest common factor of fractions 320/38, 280/787.

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 320/38,280/787?

Given fractions are 320/38,280/787

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 320/38,280/787, numerators are 320,280

Denominators are 38,787

The GCF of 320,280 is 40 .

LCM of 38,787 is 29906.

The greatest common factor of 320/38,280/787 = [GCF of 320,280]/[LCM of 38,787]= 40/29906

Therefore, the GCF of 320/38,280/787 is 40/29906.

Greatest Common Factor of 320,280

To find the highest common factor of 320,280, we have to find the factors of both numbers and list the highest common factor.

The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320

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

The HCF of 320,280 is 40.

Lets's calculate GCF of 320,280

Greatest Common Factor (GCF) of 320,280 By Common Division

2	320, 280
2	160, 140
2	80, 70
5	40, 35
	8, 7

∴ So the GCF of the given numbers is 2 x 2 x 2 x 5 = 40

Greatest Common Factor of 320,280 By Matching Biggest Common Factor Method

Now, list down the factors of 320

1,2,4,5,8,10,16,20,32,40,64,80,160,320

Now, list down the factors of 280

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

Greatest Common Factor

We found the factors 320,280 . The biggest common factor number is the GCF number.
So the greatest common factor 320,280 is 40.

Lets's calculate LCM of 38,787

Lowest Common Multiple of 38,787 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 29906

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 40/29906

Therefore, the GCF of Fractions 320/38,280/787 is 40/29906

Least Common Multiple of 38,787 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 38,787 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(38,787) = 1

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

GCF(38,787) x common factors =1 x 1 = 1

LCM(38,787) = ( 38 × 787 ) / 1

LCM(38,787) = 29906 / 1

LCM(38,787) = 29906

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FAQs on GCF of Fractions of 320/38, 280/787

1. What is the HCF of 320,280?

The HCF of 320,280 is 40

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 320/38, 280/787?

Answer: GCF of Numerators as per given numbers 320/38, 280/787 is

GCF of Numerators i.e. for 320,280 is 40

LCM of denominators i.e. for 38,787 is 29906.

Thus, GCF of Fractions is 40/29906.Finally, GCF of Fractions for 320/38, 280/787 is 40/29906.