Greatest Common Factor of 402/45, 580/414

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 402/45, 580/414

Enter two or more fractions separated by "commas"

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

GCF of:

Greatest Common Factor of 402/45,580/414

Given fractions are 402/45,580/414

Formula to find GCF of Fractions is

GCF = GCF of Numerators/LCM of Denominators

As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators

In the given fractions GCF of Numerators means GCF of 402,580

Greatest Common Factor of Numerators i.e. GCF of 402,580 is 2 .

LCM of Denominators means LCM of 45,414 as per the given fractions.

LCM of 45,414 is 2070 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 402,580

GCF of Fractions 402/45,580/414 is 2/2070

2 402, 580
201, 290

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 402,580 By Matching Biggest Common Factor Method

Greatest Common Factor of 402,580 By Matching Biggest Common Factor Method

Factors of 402

List of positive integer factors of 402 that divides 402 without a remainder.

1,2,3,6,67,134,201,402

Factors of 580

List of positive integer factors of 580 that divides 580 without a remainder.

1,2,4,5,10,20,29,58,116,145,290,580

Greatest Common Factor

We found the factors 402,580 . The biggest common factor number is the GCF number.
So the greatest common factor 402,580 is 2.

Lets's calculate LCM of 45,414

3 45, 414
3 15, 138
5, 46

∴ So the LCM of the given numbers is 3 x 3 x 5 x 46 = 2070

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2070

Therefore, the GCF of Fractions 402/45,580/414 is 2/2070

Least Common Multiple of 45,414 with GCF Formula

Least Common Multiple of 45,414 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 45,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(45,414) = 9

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

GCF(45,414) x common factors =9 x 1 = 9

LCM(45,414) = ( 45 × 414 ) / 9

LCM(45,414) = 18630 / 9

LCM(45,414) = 2070


GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

Frequently Asked Questions on Fractional GCF of 402/45, 580/414

1. 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.

2. What is the GCF of Fractions for 402/45, 580/414?

Answer: GCF of Numerators as per given numbers 402/45, 580/414 is

GCF of Numerators i.e. for 402,580 is 2

LCM of denominators i.e. for 45,414 is 2070.

Thus, GCF of Fractions is 2/2070.Finally, GCF of Fractions for 402/45, 580/414 is 2/2070.