Greatest Common Factor of 46/45, 42/54, 34/27, 470/14

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 46/45, 42/54, 34/27, 470/14

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 46/45,42/54,34/27,470/14

Given fractions are 46/45,42/54,34/27,470/14

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 46,42,34,470

Greatest Common Factor of Numerators i.e. GCF of 46,42,34,470 is 2 .

LCM of Denominators means LCM of 45,54,27,14 as per the given fractions.

LCM of 45,54,27,14 is 1890 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 46,42,34,470

GCF of Fractions 46/45,42/54,34/27,470/14 is 2/1890

2 46, 42, 34, 470
23, 21, 17, 235

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

Greatest Common Factor of 46,42,34,470 By Matching Biggest Common Factor Method

Greatest Common Factor of 46,42,34,470 By Matching Biggest Common Factor Method

Factors of 46

List of positive integer factors of 46 that divides 46 without a remainder.

1,2,23,46

Factors of 42

List of positive integer factors of 42 that divides 42 without a remainder.

1,2,3,6,7,14,21,42

Factors of 34

List of positive integer factors of 34 that divides 34 without a remainder.

1,2,17,34

Factors of 470

List of positive integer factors of 470 that divides 470 without a remainder.

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

Greatest Common Factor

We found the factors 46,42,34,470 . The biggest common factor number is the GCF number.
So the greatest common factor 46,42,34,470 is 2.

Lets's calculate LCM of 45,54,27,14

2 45, 54, 27, 14
3 45, 27, 27, 7
3 15, 9, 9, 7
3 5, 3, 3, 7
5, 1, 1, 7

∴ So the LCM of the given numbers is 2 x 3 x 3 x 3 x 5 x 1 x 1 x 7 = 1890

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1890

Therefore, the GCF of Fractions 46/45,42/54,34/27,470/14 is 2/1890

Least Common Multiple of 45,54,27,14 with GCF Formula

Least Common Multiple of 45,54,27,14 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 45,54,27,14 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(45,54,27,14) = 1

common factors(in case of two or more numbers have common factors) = 486

GCF(45,54,27,14) x common factors =1 x 486 = 486

LCM(45,54,27,14) = ( 45 × 54 × 27 × 14 ) / 486

LCM(45,54,27,14) = 918540 / 486

LCM(45,54,27,14) = 1890


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 46/45, 42/54, 34/27, 470/14

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 46/45, 42/54, 34/27, 470/14?

Answer: GCF of Numerators as per given numbers 46/45, 42/54, 34/27, 470/14 is

GCF of Numerators i.e. for 46,42,34,470 is 2

LCM of denominators i.e. for 45,54,27,14 is 1890.

Thus, GCF of Fractions is 2/1890.Finally, GCF of Fractions for 46/45, 42/54, 34/27, 470/14 is 2/1890.