How to Find GCF of 510/84, 470/2950?

GCF of 510/84, 470/2950

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 510/84, 470/2950 i.e 10/123900 easily. The following is the detailed procedure to determine the greatest common factor of fractions 510/84, 470/2950.

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 510/84,470/2950?

Given fractions are 510/84,470/2950

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 510/84,470/2950, numerators are 510,470

Denominators are 84,2950

The GCF of 510,470 is 10 .

LCM of 84,2950 is 123900.

The greatest common factor of 510/84,470/2950 = [GCF of 510,470]/[LCM of 84,2950]= 10/123900

Therefore, the GCF of 510/84,470/2950 is 10/123900.

Greatest Common Factor of 510,470

To find the highest common factor of 510,470, 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 470 are 1, 2, 5, 10, 47, 94, 235, 470

The HCF of 510,470 is 10.

Lets's calculate GCF of 510,470

Greatest Common Factor (GCF) of 510,470 By Common Division

2	510, 470
5	255, 235
	51, 47

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

Greatest Common Factor of 510,470 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 470

1,2,5,10,47,94,235,470

Greatest Common Factor

We found the factors 510,470 . The biggest common factor number is the GCF number.
So the greatest common factor 510,470 is 10.

Lets's calculate LCM of 84,2950

Lowest Common Multiple of 84,2950 using Common Division

2	84, 2950
	42, 1475

∴ So the LCM of the given numbers is 2 x 42 x 1475 = 123900

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/123900

Therefore, the GCF of Fractions 510/84,470/2950 is 10/123900

Least Common Multiple of 84,2950 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 84,2950 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(84,2950) = 2

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

GCF(84,2950) x common factors =2 x 1 = 2

LCM(84,2950) = ( 84 × 2950 ) / 2

LCM(84,2950) = 247800 / 2

LCM(84,2950) = 123900

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FAQs on GCF of Fractions of 510/84, 470/2950

1. What is the HCF of 510,470?

The HCF of 510,470 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 510/84, 470/2950?

Answer: GCF of Numerators as per given numbers 510/84, 470/2950 is

GCF of Numerators i.e. for 510,470 is 10

LCM of denominators i.e. for 84,2950 is 123900.

Thus, GCF of Fractions is 10/123900.Finally, GCF of Fractions for 510/84, 470/2950 is 10/123900.