How to Find GCF of 519/470, 5646/460?

GCF of 519/470, 5646/460

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 519/470, 5646/460 i.e 3/21620 easily. The following is the detailed procedure to determine the greatest common factor of fractions 519/470, 5646/460.

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 519/470,5646/460?

Given fractions are 519/470,5646/460

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 519/470,5646/460, numerators are 519,5646

Denominators are 470,460

The GCF of 519,5646 is 3 .

LCM of 470,460 is 21620.

The greatest common factor of 519/470,5646/460 = [GCF of 519,5646]/[LCM of 470,460]= 3/21620

Therefore, the GCF of 519/470,5646/460 is 3/21620.

Greatest Common Factor of 519,5646

To find the highest common factor of 519,5646, we have to find the factors of both numbers and list the highest common factor.

The factors of 519 are 1, 3, 173, 519

The factors of 5646 are 1, 2, 3, 6, 941, 1882, 2823, 5646

The HCF of 519,5646 is 3.

Lets's calculate GCF of 519,5646

Greatest Common Factor (GCF) of 519,5646 By Common Division

3	519, 5646
	173, 1882

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 519,5646 By Matching Biggest Common Factor Method

Now, list down the factors of 519

1,3,173,519

Now, list down the factors of 5646

1,2,3,6,941,1882,2823,5646

Greatest Common Factor

We found the factors 519,5646 . The biggest common factor number is the GCF number.
So the greatest common factor 519,5646 is 3.

Lets's calculate LCM of 470,460

Lowest Common Multiple of 470,460 using Common Division

2	470, 460
5	235, 230
	47, 46

∴ So the LCM of the given numbers is 2 x 5 x 47 x 46 = 21620

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/21620

Therefore, the GCF of Fractions 519/470,5646/460 is 3/21620

Least Common Multiple of 470,460 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 470,460 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(470,460) = 10

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

GCF(470,460) x common factors =10 x 1 = 10

LCM(470,460) = ( 470 × 460 ) / 10

LCM(470,460) = 216200 / 10

LCM(470,460) = 21620

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FAQs on GCF of Fractions of 519/470, 5646/460

1. What is the HCF of 519,5646?

The HCF of 519,5646 is 3

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 519/470, 5646/460?

Answer: GCF of Numerators as per given numbers 519/470, 5646/460 is

GCF of Numerators i.e. for 519,5646 is 3

LCM of denominators i.e. for 470,460 is 21620.

Thus, GCF of Fractions is 3/21620.Finally, GCF of Fractions for 519/470, 5646/460 is 3/21620.