Greatest Common Factor of 345/40, 640/414

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 345/40, 640/414

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 345/40,640/414

Given fractions are 345/40,640/414

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 345,640

Greatest Common Factor of Numerators i.e. GCF of 345,640 is 5 .

LCM of Denominators means LCM of 40,414 as per the given fractions.

LCM of 40,414 is 8280 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 345,640

GCF of Fractions 345/40,640/414 is 5/8280

5 345, 640
69, 128

∴ So the GCF of the given numbers is 5 = 5

Greatest Common Factor of 345,640 By Matching Biggest Common Factor Method

Greatest Common Factor of 345,640 By Matching Biggest Common Factor Method

Factors of 345

List of positive integer factors of 345 that divides 345 without a remainder.

1,3,5,15,23,69,115,345

Factors of 640

List of positive integer factors of 640 that divides 640 without a remainder.

1,2,4,5,8,10,16,20,32,40,64,80,128,160,320,640

Greatest Common Factor

We found the factors 345,640 . The biggest common factor number is the GCF number.
So the greatest common factor 345,640 is 5.

Lets's calculate LCM of 40,414

2 40, 414
20, 207

∴ So the LCM of the given numbers is 2 x 20 x 207 = 8280

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/8280

Therefore, the GCF of Fractions 345/40,640/414 is 5/8280

Least Common Multiple of 40,414 with GCF Formula

Least Common Multiple of 40,414 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 40,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(40,414) = 2

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

GCF(40,414) x common factors =2 x 1 = 2

LCM(40,414) = ( 40 × 414 ) / 2

LCM(40,414) = 16560 / 2

LCM(40,414) = 8280


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 345/40, 640/414

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 345/40, 640/414?

Answer: GCF of Numerators as per given numbers 345/40, 640/414 is

GCF of Numerators i.e. for 345,640 is 5

LCM of denominators i.e. for 40,414 is 8280.

Thus, GCF of Fractions is 5/8280.Finally, GCF of Fractions for 345/40, 640/414 is 5/8280.