Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 75/70,49/65,41/63,701/96
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 75,49,41,701
Greatest Common Factor of Numerators i.e. GCF of 75,49,41,701 is 1 .
LCM of Denominators means LCM of 70,65,63,96 as per the given fractions.
LCM of 70,65,63,96 is 131040 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 75,49,41,701
∴ 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 49
List of positive integer factors of 49 that divides 49 without a remainder.
1,7,49
Factors of 41
List of positive integer factors of 41 that divides 41 without a remainder.
1,41
Factors of 701
List of positive integer factors of 701 that divides 701 without a remainder.
1,701
Greatest Common Factor
We found the factors 75,49,41,701 . The biggest common factor number is the GCF number.
So the greatest common factor 75,49,41,701 is 1.
Lets's calculate LCM of 70,65,63,96
2 | 70, 65, 63, 96 |
3 | 35, 65, 63, 48 |
5 | 35, 65, 21, 16 |
7 | 7, 13, 21, 16 |
1, 13, 3, 16 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 7 x 1 x 13 x 3 x 16 = 131040
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/131040
Therefore, the GCF of Fractions 75/70,49/65,41/63,701/96 is 1/131040
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 70,65,63,96 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(70,65,63,96) = 1
common factors(in case of two or more numbers have common factors) = 210
GCF(70,65,63,96) x common factors =1 x 210 = 210
LCM(70,65,63,96) = ( 70 × 65 × 63 × 96 ) / 210
LCM(70,65,63,96) = 27518400 / 210
LCM(70,65,63,96) = 131040
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 75/70, 49/65, 41/63, 701/96?
Answer: GCF of Numerators as per given numbers 75/70, 49/65, 41/63, 701/96 is
GCF of Numerators i.e. for 75,49,41,701 is 1
LCM of denominators i.e. for 70,65,63,96 is 131040.
Thus, GCF of Fractions is 1/131040.Finally, GCF of Fractions for 75/70, 49/65, 41/63, 701/96 is 1/131040.