How to Find GCF of 960/219, 820/113?

GCF of 960/219, 820/113

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 960/219, 820/113 i.e 20/24747 easily. The following is the detailed procedure to determine the greatest common factor of fractions 960/219, 820/113.

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 960/219,820/113?

Given fractions are 960/219,820/113

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 960/219,820/113, numerators are 960,820

Denominators are 219,113

The GCF of 960,820 is 20 .

LCM of 219,113 is 24747.

The greatest common factor of 960/219,820/113 = [GCF of 960,820]/[LCM of 219,113]= 20/24747

Therefore, the GCF of 960/219,820/113 is 20/24747.

Greatest Common Factor of 960,820

To find the highest common factor of 960,820, we have to find the factors of both numbers and list the highest common factor.

The factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960

The factors of 820 are 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, 820

The HCF of 960,820 is 20.

Lets's calculate GCF of 960,820

Greatest Common Factor (GCF) of 960,820 By Common Division

2	960, 820
2	480, 410
5	240, 205
	48, 41

∴ So the GCF of the given numbers is 2 x 2 x 5 = 20

Greatest Common Factor of 960,820 By Matching Biggest Common Factor Method

Now, list down the factors of 960

1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,64,80,96,120,160,192,240,320,480,960

Now, list down the factors of 820

1,2,4,5,10,20,41,82,164,205,410,820

Greatest Common Factor

We found the factors 960,820 . The biggest common factor number is the GCF number.
So the greatest common factor 960,820 is 20.

Lets's calculate LCM of 219,113

Lowest Common Multiple of 219,113 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 24747

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/24747

Therefore, the GCF of Fractions 960/219,820/113 is 20/24747

Least Common Multiple of 219,113 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 219,113 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(219,113) = 1

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

GCF(219,113) x common factors =1 x 1 = 1

LCM(219,113) = ( 219 × 113 ) / 1

LCM(219,113) = 24747 / 1

LCM(219,113) = 24747

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FAQs on GCF of Fractions of 960/219, 820/113

1. What is the HCF of 960,820?

The HCF of 960,820 is 20

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 960/219, 820/113?

Answer: GCF of Numerators as per given numbers 960/219, 820/113 is

GCF of Numerators i.e. for 960,820 is 20

LCM of denominators i.e. for 219,113 is 24747.

Thus, GCF of Fractions is 20/24747.Finally, GCF of Fractions for 960/219, 820/113 is 20/24747.