How to Find GCF of 205/179, 8960/998?

GCF of 205/179, 8960/998

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 205/179, 8960/998 i.e 5/178642 easily. The following is the detailed procedure to determine the greatest common factor of fractions 205/179, 8960/998.

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 205/179,8960/998?

Given fractions are 205/179,8960/998

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 205/179,8960/998, numerators are 205,8960

Denominators are 179,998

The GCF of 205,8960 is 5 .

LCM of 179,998 is 178642.

The greatest common factor of 205/179,8960/998 = [GCF of 205,8960]/[LCM of 179,998]= 5/178642

Therefore, the GCF of 205/179,8960/998 is 5/178642.

Greatest Common Factor of 205,8960

To find the highest common factor of 205,8960, we have to find the factors of both numbers and list the highest common factor.

The factors of 205 are 1, 5, 41, 205

The factors of 8960 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 64, 70, 80, 112, 128, 140, 160, 224, 256, 280, 320, 448, 560, 640, 896, 1120, 1280, 1792, 2240, 4480, 8960

The HCF of 205,8960 is 5.

Lets's calculate GCF of 205,8960

Greatest Common Factor (GCF) of 205,8960 By Common Division

5	205, 8960
	41, 1792

∴ So the GCF of the given numbers is 5 = 5

Greatest Common Factor of 205,8960 By Matching Biggest Common Factor Method

Now, list down the factors of 205

1,5,41,205

Now, list down the factors of 8960

1,2,4,5,7,8,10,14,16,20,28,32,35,40,56,64,70,80,112,128,140,160,224,256,280,320,448,560,640,896,1120,1280,1792,2240,4480,8960

Greatest Common Factor

We found the factors 205,8960 . The biggest common factor number is the GCF number.
So the greatest common factor 205,8960 is 5.

Lets's calculate LCM of 179,998

Lowest Common Multiple of 179,998 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 178642

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/178642

Therefore, the GCF of Fractions 205/179,8960/998 is 5/178642

Least Common Multiple of 179,998 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 179,998 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(179,998) = 1

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

GCF(179,998) x common factors =1 x 1 = 1

LCM(179,998) = ( 179 × 998 ) / 1

LCM(179,998) = 178642 / 1

LCM(179,998) = 178642

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 205/179, 8960/998

1. What is the HCF of 205,8960?

The HCF of 205,8960 is 5

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 205/179, 8960/998?

Answer: GCF of Numerators as per given numbers 205/179, 8960/998 is

GCF of Numerators i.e. for 205,8960 is 5

LCM of denominators i.e. for 179,998 is 178642.

Thus, GCF of Fractions is 5/178642.Finally, GCF of Fractions for 205/179, 8960/998 is 5/178642.