Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 75/26,38/31,78/55,11/770
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 75,38,78,11
Greatest Common Factor of Numerators i.e. GCF of 75,38,78,11 is 1 .
LCM of Denominators means LCM of 26,31,55,770 as per the given fractions.
LCM of 26,31,55,770 is 310310 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 75,38,78,11
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 75
List of positive integer factors of 75 that divides 75 without a remainder.
1,3,5,15,25,75
Factors of 38
List of positive integer factors of 38 that divides 38 without a remainder.
1,2,19,38
Factors of 78
List of positive integer factors of 78 that divides 78 without a remainder.
1,2,3,6,13,26,39,78
Factors of 11
List of positive integer factors of 11 that divides 11 without a remainder.
1,11
Greatest Common Factor
We found the factors 75,38,78,11 . The biggest common factor number is the GCF number.
So the greatest common factor 75,38,78,11 is 1.
Lets's calculate LCM of 26,31,55,770
2 | 26, 31, 55, 770 |
5 | 13, 31, 55, 385 |
11 | 13, 31, 11, 77 |
13, 31, 1, 7 |
∴ So the LCM of the given numbers is 2 x 5 x 11 x 13 x 31 x 1 x 7 = 310310
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/310310
Therefore, the GCF of Fractions 75/26,38/31,78/55,11/770 is 1/310310
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 26,31,55,770 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(26,31,55,770) = 1
common factors(in case of two or more numbers have common factors) = 110
GCF(26,31,55,770) x common factors =1 x 110 = 110
LCM(26,31,55,770) = ( 26 × 31 × 55 × 770 ) / 110
LCM(26,31,55,770) = 34134100 / 110
LCM(26,31,55,770) = 310310
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 75/26, 38/31, 78/55, 11/770?
Answer: GCF of Numerators as per given numbers 75/26, 38/31, 78/55, 11/770 is
GCF of Numerators i.e. for 75,38,78,11 is 1
LCM of denominators i.e. for 26,31,55,770 is 310310.
Thus, GCF of Fractions is 1/310310.Finally, GCF of Fractions for 75/26, 38/31, 78/55, 11/770 is 1/310310.