How to Find GCF of 560/43, 272/182?

GCF of 560/43, 272/182

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 560/43, 272/182 i.e 16/7826 easily. The following is the detailed procedure to determine the greatest common factor of fractions 560/43, 272/182.

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 560/43,272/182?

Given fractions are 560/43,272/182

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 560/43,272/182, numerators are 560,272

Denominators are 43,182

The GCF of 560,272 is 16 .

LCM of 43,182 is 7826.

The greatest common factor of 560/43,272/182 = [GCF of 560,272]/[LCM of 43,182]= 16/7826

Therefore, the GCF of 560/43,272/182 is 16/7826.

Greatest Common Factor of 560,272

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

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

The HCF of 560,272 is 16.

Lets's calculate GCF of 560,272

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

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

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

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

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

Now, list down the factors of 272

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

Greatest Common Factor

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

Lets's calculate LCM of 43,182

Lowest Common Multiple of 43,182 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 7826

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/7826

Therefore, the GCF of Fractions 560/43,272/182 is 16/7826

Least Common Multiple of 43,182 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 43,182 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(43,182) = 1

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

GCF(43,182) x common factors =1 x 1 = 1

LCM(43,182) = ( 43 × 182 ) / 1

LCM(43,182) = 7826 / 1

LCM(43,182) = 7826

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 560/43, 272/182

1. What is the HCF of 560,272?

The HCF of 560,272 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 560/43, 272/182?

Answer: GCF of Numerators as per given numbers 560/43, 272/182 is

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

LCM of denominators i.e. for 43,182 is 7826.

Thus, GCF of Fractions is 16/7826.Finally, GCF of Fractions for 560/43, 272/182 is 16/7826.