Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 52/46,42/21,24/76,705/78
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 52,42,24,705
Greatest Common Factor of Numerators i.e. GCF of 52,42,24,705 is 1 .
LCM of Denominators means LCM of 46,21,76,78 as per the given fractions.
LCM of 46,21,76,78 is 477204 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 52,42,24,705
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 52
List of positive integer factors of 52 that divides 52 without a remainder.
1,2,4,13,26,52
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 24
List of positive integer factors of 24 that divides 24 without a remainder.
1,2,3,4,6,8,12,24
Factors of 705
List of positive integer factors of 705 that divides 705 without a remainder.
1,3,5,15,47,141,235,705
Greatest Common Factor
We found the factors 52,42,24,705 . The biggest common factor number is the GCF number.
So the greatest common factor 52,42,24,705 is 1.
Lets's calculate LCM of 46,21,76,78
2 | 46, 21, 76, 78 |
3 | 23, 21, 38, 39 |
23, 7, 38, 13 |
∴ So the LCM of the given numbers is 2 x 3 x 23 x 7 x 38 x 13 = 477204
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/477204
Therefore, the GCF of Fractions 52/46,42/21,24/76,705/78 is 1/477204
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 46,21,76,78 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(46,21,76,78) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(46,21,76,78) x common factors =1 x 12 = 12
LCM(46,21,76,78) = ( 46 × 21 × 76 × 78 ) / 12
LCM(46,21,76,78) = 5726448 / 12
LCM(46,21,76,78) = 477204
Here are some samples of GCF of Fractions calculations.
Here are some samples of GCF of Fractions calculations.
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 52/46, 42/21, 24/76, 705/78?
Answer: GCF of Numerators as per given numbers 52/46, 42/21, 24/76, 705/78 is
GCF of Numerators i.e. for 52,42,24,705 is 1
LCM of denominators i.e. for 46,21,76,78 is 477204.
Thus, GCF of Fractions is 1/477204.Finally, GCF of Fractions for 52/46, 42/21, 24/76, 705/78 is 1/477204.