How to Find GCF of 272/978, 560/869?

GCF of 272/978, 560/869

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 272/978, 560/869 i.e 16/849882 easily. The following is the detailed procedure to determine the greatest common factor of fractions 272/978, 560/869.

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 272/978,560/869?

Given fractions are 272/978,560/869

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 272/978,560/869, numerators are 272,560

Denominators are 978,869

The GCF of 272,560 is 16 .

LCM of 978,869 is 849882.

The greatest common factor of 272/978,560/869 = [GCF of 272,560]/[LCM of 978,869]= 16/849882

Therefore, the GCF of 272/978,560/869 is 16/849882.

Greatest Common Factor of 272,560

To find the highest common factor of 272,560, we have to find the factors of both numbers and list the highest common factor.

The factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272

The factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560

The HCF of 272,560 is 16.

Lets's calculate GCF of 272,560

Greatest Common Factor (GCF) of 272,560 By Common Division

2	272, 560
2	136, 280
2	68, 140
2	34, 70
	17, 35

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16

Greatest Common Factor of 272,560 By Matching Biggest Common Factor Method

Now, list down the factors of 272

1,2,4,8,16,17,34,68,136,272

Now, list down the factors of 560

1,2,4,5,7,8,10,14,16,20,28,35,40,56,70,80,112,140,280,560

Greatest Common Factor

We found the factors 272,560 . The biggest common factor number is the GCF number.
So the greatest common factor 272,560 is 16.

Lets's calculate LCM of 978,869

Lowest Common Multiple of 978,869 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 849882

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/849882

Therefore, the GCF of Fractions 272/978,560/869 is 16/849882

Least Common Multiple of 978,869 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 978,869 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(978,869) = 1

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

GCF(978,869) x common factors =1 x 1 = 1

LCM(978,869) = ( 978 × 869 ) / 1

LCM(978,869) = 849882 / 1

LCM(978,869) = 849882

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FAQs on GCF of Fractions of 272/978, 560/869

1. What is the HCF of 272,560?

The HCF of 272,560 is 16

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 272/978, 560/869?

Answer: GCF of Numerators as per given numbers 272/978, 560/869 is

GCF of Numerators i.e. for 272,560 is 16

LCM of denominators i.e. for 978,869 is 849882.

Thus, GCF of Fractions is 16/849882.Finally, GCF of Fractions for 272/978, 560/869 is 16/849882.