Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 60/72,55/84,71/64,283/49
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 60,55,71,283
Greatest Common Factor of Numerators i.e. GCF of 60,55,71,283 is 1 .
LCM of Denominators means LCM of 72,84,64,49 as per the given fractions.
LCM of 72,84,64,49 is 28224 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 60,55,71,283
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 60
List of positive integer factors of 60 that divides 60 without a remainder.
1,2,3,4,5,6,10,12,15,20,30,60
Factors of 55
List of positive integer factors of 55 that divides 55 without a remainder.
1,5,11,55
Factors of 71
List of positive integer factors of 71 that divides 71 without a remainder.
1,71
Factors of 283
List of positive integer factors of 283 that divides 283 without a remainder.
1,283
Greatest Common Factor
We found the factors 60,55,71,283 . The biggest common factor number is the GCF number.
So the greatest common factor 60,55,71,283 is 1.
Lets's calculate LCM of 72,84,64,49
2 | 72, 84, 64, 49 |
2 | 36, 42, 32, 49 |
2 | 18, 21, 16, 49 |
3 | 9, 21, 8, 49 |
7 | 3, 7, 8, 49 |
3, 1, 8, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 7 x 3 x 1 x 8 x 7 = 28224
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/28224
Therefore, the GCF of Fractions 60/72,55/84,71/64,283/49 is 1/28224
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 72,84,64,49 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(72,84,64,49) = 1
common factors(in case of two or more numbers have common factors) = 672
GCF(72,84,64,49) x common factors =1 x 672 = 672
LCM(72,84,64,49) = ( 72 × 84 × 64 × 49 ) / 672
LCM(72,84,64,49) = 18966528 / 672
LCM(72,84,64,49) = 28224
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 60/72, 55/84, 71/64, 283/49?
Answer: GCF of Numerators as per given numbers 60/72, 55/84, 71/64, 283/49 is
GCF of Numerators i.e. for 60,55,71,283 is 1
LCM of denominators i.e. for 72,84,64,49 is 28224.
Thus, GCF of Fractions is 1/28224.Finally, GCF of Fractions for 60/72, 55/84, 71/64, 283/49 is 1/28224.