Greatest Common Factor of 34/69, 40/51, 30/94, 10/106

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 34/69, 40/51, 30/94, 10/106

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 34/69,40/51,30/94,10/106

Given fractions are 34/69,40/51,30/94,10/106

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 34,40,30,10

Greatest Common Factor of Numerators i.e. GCF of 34,40,30,10 is 2 .

LCM of Denominators means LCM of 69,51,94,106 as per the given fractions.

LCM of 69,51,94,106 is 5843886 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 34,40,30,10

GCF of Fractions 34/69,40/51,30/94,10/106 is 2/5843886

2 34, 40, 30, 10
17, 20, 15, 5

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

Greatest Common Factor of 34,40,30,10 By Matching Biggest Common Factor Method

Greatest Common Factor of 34,40,30,10 By Matching Biggest Common Factor Method

Factors of 34

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

1,2,17,34

Factors of 40

List of positive integer factors of 40 that divides 40 without a remainder.

1,2,4,5,8,10,20,40

Factors of 30

List of positive integer factors of 30 that divides 30 without a remainder.

1,2,3,5,6,10,15,30

Factors of 10

List of positive integer factors of 10 that divides 10 without a remainder.

1,2,5,10

Greatest Common Factor

We found the factors 34,40,30,10 . The biggest common factor number is the GCF number.
So the greatest common factor 34,40,30,10 is 2.

Lets's calculate LCM of 69,51,94,106

2 69, 51, 94, 106
3 69, 51, 47, 53
23, 17, 47, 53

∴ So the LCM of the given numbers is 2 x 3 x 23 x 17 x 47 x 53 = 5843886

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/5843886

Therefore, the GCF of Fractions 34/69,40/51,30/94,10/106 is 2/5843886

Least Common Multiple of 69,51,94,106 with GCF Formula

Least Common Multiple of 69,51,94,106 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 69,51,94,106 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(69,51,94,106) = 1

common factors(in case of two or more numbers have common factors) = 6

GCF(69,51,94,106) x common factors =1 x 6 = 6

LCM(69,51,94,106) = ( 69 × 51 × 94 × 106 ) / 6

LCM(69,51,94,106) = 35063316 / 6

LCM(69,51,94,106) = 5843886


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 34/69, 40/51, 30/94, 10/106

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 34/69, 40/51, 30/94, 10/106?

Answer: GCF of Numerators as per given numbers 34/69, 40/51, 30/94, 10/106 is

GCF of Numerators i.e. for 34,40,30,10 is 2

LCM of denominators i.e. for 69,51,94,106 is 5843886.

Thus, GCF of Fractions is 2/5843886.Finally, GCF of Fractions for 34/69, 40/51, 30/94, 10/106 is 2/5843886.