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GCF of 510/20, 940/784

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 510/20, 940/784 i.e 10/3920 easily. The following is the detailed procedure to determine the greatest common factor of fractions 510/20, 940/784.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 510/20,940/784?

Given fractions are 510/20,940/784

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 510/20,940/784, numerators are 510,940

Denominators are 20,784

The GCF of 510,940 is 10 .

LCM of 20,784 is 3920.

The greatest common factor of 510/20,940/784 = [GCF of 510,940]/[LCM of 20,784]= 10/3920

Therefore, the GCF of 510/20,940/784 is 10/3920.

Greatest Common Factor of 510,940

To find the highest common factor of 510,940, we have to find the factors of both numbers and list the highest common factor.

The factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510

The factors of 940 are 1, 2, 4, 5, 10, 20, 47, 94, 188, 235, 470, 940

The HCF of 510,940 is 10.

Lets's calculate GCF of 510,940

Greatest Common Factor (GCF) of 510,940 By Common Division

2 510, 940
5 255, 470
51, 94

∴ So the GCF of the given numbers is 2 x 5 = 10

Greatest Common Factor of 510,940 By Matching Biggest Common Factor Method

Greatest Common Factor of 510,940 By Matching Biggest Common Factor Method

Now, list down the factors of 510

:

1,2,3,5,6,10,15,17,30,34,51,85,102,170,255,510

Now, list down the factors of 940

:

1,2,4,5,10,20,47,94,188,235,470,940

Greatest Common Factor

We found the factors 510,940 . The biggest common factor number is the GCF number.
So the greatest common factor 510,940 is 10.

Lets's calculate LCM of 20,784

Lowest Common Multiple of 20,784 using Common Division

2 20, 784
2 10, 392
5, 196

∴ So the LCM of the given numbers is 2 x 2 x 5 x 196 = 3920

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/3920

Therefore, the GCF of Fractions 510/20,940/784 is 10/3920

Least Common Multiple of 20,784 with GCF Formula

Least Common Multiple of 20,784 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 20,784 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(20,784) = 4

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

GCF(20,784) x common factors =4 x 1 = 4

LCM(20,784) = ( 20 × 784 ) / 4

LCM(20,784) = 15680 / 4

LCM(20,784) = 3920


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FAQs on GCF of Fractions of 510/20, 940/784

1. What is the HCF of 510,940?

The HCF of 510,940 is 10

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 510/20, 940/784?

Answer: GCF of Numerators as per given numbers 510/20, 940/784 is

GCF of Numerators i.e. for 510,940 is 10

LCM of denominators i.e. for 20,784 is 3920.

Thus, GCF of Fractions is 10/3920.Finally, GCF of Fractions for 510/20, 940/784 is 10/3920.