Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 67/87,75/33,86/84,80/98
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 67,75,86,80
Greatest Common Factor of Numerators i.e. GCF of 67,75,86,80 is 1 .
LCM of Denominators means LCM of 87,33,84,98 as per the given fractions.
LCM of 87,33,84,98 is 187572 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 67,75,86,80
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 67
List of positive integer factors of 67 that divides 67 without a remainder.
1,67
Factors of 75
List of positive integer factors of 75 that divides 75 without a remainder.
1,3,5,15,25,75
Factors of 86
List of positive integer factors of 86 that divides 86 without a remainder.
1,2,43,86
Factors of 80
List of positive integer factors of 80 that divides 80 without a remainder.
1,2,4,5,8,10,16,20,40,80
Greatest Common Factor
We found the factors 67,75,86,80 . The biggest common factor number is the GCF number.
So the greatest common factor 67,75,86,80 is 1.
Lets's calculate LCM of 87,33,84,98
2 | 87, 33, 84, 98 |
3 | 87, 33, 42, 49 |
7 | 29, 11, 14, 49 |
29, 11, 2, 7 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 29 x 11 x 2 x 7 = 187572
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/187572
Therefore, the GCF of Fractions 67/87,75/33,86/84,80/98 is 1/187572
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 87,33,84,98 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(87,33,84,98) = 1
common factors(in case of two or more numbers have common factors) = 126
GCF(87,33,84,98) x common factors =1 x 126 = 126
LCM(87,33,84,98) = ( 87 × 33 × 84 × 98 ) / 126
LCM(87,33,84,98) = 23634072 / 126
LCM(87,33,84,98) = 187572
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 67/87, 75/33, 86/84, 80/98?
Answer: GCF of Numerators as per given numbers 67/87, 75/33, 86/84, 80/98 is
GCF of Numerators i.e. for 67,75,86,80 is 1
LCM of denominators i.e. for 87,33,84,98 is 187572.
Thus, GCF of Fractions is 1/187572.Finally, GCF of Fractions for 67/87, 75/33, 86/84, 80/98 is 1/187572.