Greatest Common Factor of 74/2, 89/1, 74/8, 66/5, 518/2, 56/8, 46/7, 578/9, 71/3, 85/3

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 74/2, 89/1, 74/8, 66/5, 518/2, 56/8, 46/7, 578/9, 71/3, 85/3

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 74/2,89/1,74/8,66/5,518/2,56/8,46/7,578/9,71/3,85/3

Given fractions are 74/2,89/1,74/8,66/5,518/2,56/8,46/7,578/9,71/3,85/3

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 74,89,74,66,518,56,46,578,71,85

Greatest Common Factor of Numerators i.e. GCF of 74,89,74,66,518,56,46,578,71,85 is 1 .

LCM of Denominators means LCM of 2,1,8,5,2,8,7,9,3,3 as per the given fractions.

LCM of 2,1,8,5,2,8,7,9,3,3 is 2520 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 74,89,74,66,518,56,46,578,71,85

GCF of Fractions 74/2,89/1,74/8,66/5,518/2,56/8,46/7,578/9,71/3,85/3 is 1/2520

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

Greatest Common Factor of 74,89,74,66,518,56,46,578,71,85 By Matching Biggest Common Factor Method

Greatest Common Factor of 74,89,74,66,518,56,46,578,71,85 By Matching Biggest Common Factor Method

Factors of 74

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

1,2,37,74

Factors of 89

List of positive integer factors of 89 that divides 89 without a remainder.

1,89

Factors of 74

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

1,2,37,74

Factors of 66

List of positive integer factors of 66 that divides 66 without a remainder.

1,2,3,6,11,22,33,66

Factors of 518

List of positive integer factors of 518 that divides 518 without a remainder.

1,2,7,14,37,74,259,518

Factors of 56

List of positive integer factors of 56 that divides 56 without a remainder.

1,2,4,7,8,14,28,56

Factors of 46

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

1,2,23,46

Factors of 578

List of positive integer factors of 578 that divides 578 without a remainder.

1,2,17,34,289,578

Factors of 71

List of positive integer factors of 71 that divides 71 without a remainder.

1,71

Factors of 85

List of positive integer factors of 85 that divides 85 without a remainder.

1,5,17,85

Greatest Common Factor

We found the factors 74,89,74,66,518,56,46,578,71,85 . The biggest common factor number is the GCF number.
So the greatest common factor 74,89,74,66,518,56,46,578,71,85 is 1.

Lets's calculate LCM of 2,1,8,5,2,8,7,9,3,3

2 2, 1, 8, 5, 2, 8, 7, 9, 3, 3
2 1, 1, 4, 5, 1, 4, 7, 9, 3, 3
2 1, 1, 2, 5, 1, 2, 7, 9, 3, 3
3 1, 1, 1, 5, 1, 1, 7, 9, 3, 3
1, 1, 1, 5, 1, 1, 7, 1, 1, 3

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 1 x 1 x 1 x 5 x 1 x 1 x 7 x 1 x 1 x 3 = 2520

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2520

Therefore, the GCF of Fractions 74/2,89/1,74/8,66/5,518/2,56/8,46/7,578/9,71/3,85/3 is 1/2520

Least Common Multiple of 2,1,8,5,2,8,7,9,3,3 with GCF Formula

Least Common Multiple of 2,1,8,5,2,8,7,9,3,3 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 2,1,8,5,2,8,7,9,3,3 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(2,1,8,5,2,8,7,9,3,3) = 1

common factors(in case of two or more numbers have common factors) = 288

GCF(2,1,8,5,2,8,7,9,3,3) x common factors =1 x 288 = 288

LCM(2,1,8,5,2,8,7,9,3,3) = ( 2 × 1 × 8 × 5 × 2 × 8 × 7 × 9 × 3 × 3 ) / 288

LCM(2,1,8,5,2,8,7,9,3,3) = 725760 / 288

LCM(2,1,8,5,2,8,7,9,3,3) = 2520


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 74/2, 89/1, 74/8, 66/5, 518/2, 56/8, 46/7, 578/9, 71/3, 85/3

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 74/2, 89/1, 74/8, 66/5, 518/2, 56/8, 46/7, 578/9, 71/3, 85/3?

Answer: GCF of Numerators as per given numbers 74/2, 89/1, 74/8, 66/5, 518/2, 56/8, 46/7, 578/9, 71/3, 85/3 is

GCF of Numerators i.e. for 74,89,74,66,518,56,46,578,71,85 is 1

LCM of denominators i.e. for 2,1,8,5,2,8,7,9,3,3 is 2520.

Thus, GCF of Fractions is 1/2520.Finally, GCF of Fractions for 74/2, 89/1, 74/8, 66/5, 518/2, 56/8, 46/7, 578/9, 71/3, 85/3 is 1/2520.