Greatest Common Factor of 41/8, 45/1, 74/2, 69/5, 989/8, 27/9, 75/9, 310/5, 98/3, 99/3

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 41/8, 45/1, 74/2, 69/5, 989/8, 27/9, 75/9, 310/5, 98/3, 99/3

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 41/8,45/1,74/2,69/5,989/8,27/9,75/9,310/5,98/3,99/3

Given fractions are 41/8,45/1,74/2,69/5,989/8,27/9,75/9,310/5,98/3,99/3

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 41,45,74,69,989,27,75,310,98,99

Greatest Common Factor of Numerators i.e. GCF of 41,45,74,69,989,27,75,310,98,99 is 1 .

LCM of Denominators means LCM of 8,1,2,5,8,9,9,5,3,3 as per the given fractions.

LCM of 8,1,2,5,8,9,9,5,3,3 is 360 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 41,45,74,69,989,27,75,310,98,99

GCF of Fractions 41/8,45/1,74/2,69/5,989/8,27/9,75/9,310/5,98/3,99/3 is 1/360

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 41,45,74,69,989,27,75,310,98,99 By Matching Biggest Common Factor Method

Greatest Common Factor of 41,45,74,69,989,27,75,310,98,99 By Matching Biggest Common Factor Method

Factors of 41

List of positive integer factors of 41 that divides 41 without a remainder.

1,41

Factors of 45

List of positive integer factors of 45 that divides 45 without a remainder.

1,3,5,9,15,45

Factors of 74

List of positive integer factors of 74 that divides 74 without a remainder.

1,2,37,74

Factors of 69

List of positive integer factors of 69 that divides 69 without a remainder.

1,3,23,69

Factors of 989

List of positive integer factors of 989 that divides 989 without a remainder.

1,23,43,989

Factors of 27

List of positive integer factors of 27 that divides 27 without a remainder.

1,3,9,27

Factors of 75

List of positive integer factors of 75 that divides 75 without a remainder.

1,3,5,15,25,75

Factors of 310

List of positive integer factors of 310 that divides 310 without a remainder.

1,2,5,10,31,62,155,310

Factors of 98

List of positive integer factors of 98 that divides 98 without a remainder.

1,2,7,14,49,98

Factors of 99

List of positive integer factors of 99 that divides 99 without a remainder.

1,3,9,11,33,99

Greatest Common Factor

We found the factors 41,45,74,69,989,27,75,310,98,99 . The biggest common factor number is the GCF number.
So the greatest common factor 41,45,74,69,989,27,75,310,98,99 is 1.

Lets's calculate LCM of 8,1,2,5,8,9,9,5,3,3

2 8, 1, 2, 5, 8, 9, 9, 5, 3, 3
2 4, 1, 1, 5, 4, 9, 9, 5, 3, 3
2 2, 1, 1, 5, 2, 9, 9, 5, 3, 3
3 1, 1, 1, 5, 1, 9, 9, 5, 3, 3
3 1, 1, 1, 5, 1, 1, 1, 5, 3, 3
5 1, 1, 1, 5, 1, 1, 1, 5, 1, 1
1, 1, 1, 1, 1, 1, 1, 1, 1, 1

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 3 x 5 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 = 360

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/360

Therefore, the GCF of Fractions 41/8,45/1,74/2,69/5,989/8,27/9,75/9,310/5,98/3,99/3 is 1/360

Least Common Multiple of 8,1,2,5,8,9,9,5,3,3 with GCF Formula

Least Common Multiple of 8,1,2,5,8,9,9,5,3,3 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 8,1,2,5,8,9,9,5,3,3 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(8,1,2,5,8,9,9,5,3,3) = 1

common factors(in case of two or more numbers have common factors) = 6480

GCF(8,1,2,5,8,9,9,5,3,3) x common factors =1 x 6480 = 6480

LCM(8,1,2,5,8,9,9,5,3,3) = ( 8 × 1 × 2 × 5 × 8 × 9 × 9 × 5 × 3 × 3 ) / 6480

LCM(8,1,2,5,8,9,9,5,3,3) = 2332800 / 6480

LCM(8,1,2,5,8,9,9,5,3,3) = 360


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 41/8, 45/1, 74/2, 69/5, 989/8, 27/9, 75/9, 310/5, 98/3, 99/3

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 41/8, 45/1, 74/2, 69/5, 989/8, 27/9, 75/9, 310/5, 98/3, 99/3?

Answer: GCF of Numerators as per given numbers 41/8, 45/1, 74/2, 69/5, 989/8, 27/9, 75/9, 310/5, 98/3, 99/3 is

GCF of Numerators i.e. for 41,45,74,69,989,27,75,310,98,99 is 1

LCM of denominators i.e. for 8,1,2,5,8,9,9,5,3,3 is 360.

Thus, GCF of Fractions is 1/360.Finally, GCF of Fractions for 41/8, 45/1, 74/2, 69/5, 989/8, 27/9, 75/9, 310/5, 98/3, 99/3 is 1/360.