Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 69/56,80/12,71/84,84/88
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 69,80,71,84
Greatest Common Factor of Numerators i.e. GCF of 69,80,71,84 is 1 .
LCM of Denominators means LCM of 56,12,84,88 as per the given fractions.
LCM of 56,12,84,88 is 1848 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 69,80,71,84
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 69
List of positive integer factors of 69 that divides 69 without a remainder.
1,3,23,69
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
Factors of 71
List of positive integer factors of 71 that divides 71 without a remainder.
1,71
Factors of 84
List of positive integer factors of 84 that divides 84 without a remainder.
1,2,3,4,6,7,12,14,21,28,42,84
Greatest Common Factor
We found the factors 69,80,71,84 . The biggest common factor number is the GCF number.
So the greatest common factor 69,80,71,84 is 1.
Lets's calculate LCM of 56,12,84,88
2 | 56, 12, 84, 88 |
2 | 28, 6, 42, 44 |
2 | 14, 3, 21, 22 |
3 | 7, 3, 21, 11 |
7 | 7, 1, 7, 11 |
1, 1, 1, 11 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 7 x 1 x 1 x 1 x 11 = 1848
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1848
Therefore, the GCF of Fractions 69/56,80/12,71/84,84/88 is 1/1848
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 56,12,84,88 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(56,12,84,88) = 4
common factors(in case of two or more numbers have common factors) = 672
GCF(56,12,84,88) x common factors =4 x 672 = 2688
LCM(56,12,84,88) = ( 56 × 12 × 84 × 88 ) / 2688
LCM(56,12,84,88) = 4967424 / 2688
LCM(56,12,84,88) = 1848
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 69/56, 80/12, 71/84, 84/88?
Answer: GCF of Numerators as per given numbers 69/56, 80/12, 71/84, 84/88 is
GCF of Numerators i.e. for 69,80,71,84 is 1
LCM of denominators i.e. for 56,12,84,88 is 1848.
Thus, GCF of Fractions is 1/1848.Finally, GCF of Fractions for 69/56, 80/12, 71/84, 84/88 is 1/1848.