Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 64/69,80/61,72/82,164/62
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 64,80,72,164
Greatest Common Factor of Numerators i.e. GCF of 64,80,72,164 is 4 .
LCM of Denominators means LCM of 69,61,82,62 as per the given fractions.
LCM of 69,61,82,62 is 10699278 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 64,80,72,164
2 | 64, 80, 72, 164 |
2 | 32, 40, 36, 82 |
16, 20, 18, 41 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Factors of 64
List of positive integer factors of 64 that divides 64 without a remainder.
1,2,4,8,16,32,64
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 72
List of positive integer factors of 72 that divides 72 without a remainder.
1,2,3,4,6,8,9,12,18,24,36,72
Factors of 164
List of positive integer factors of 164 that divides 164 without a remainder.
1,2,4,41,82,164
Greatest Common Factor
We found the factors 64,80,72,164 . The biggest common factor number is the GCF number.
So the greatest common factor 64,80,72,164 is 4.
Lets's calculate LCM of 69,61,82,62
2 | 69, 61, 82, 62 |
69, 61, 41, 31 |
∴ So the LCM of the given numbers is 2 x 69 x 61 x 41 x 31 = 10699278
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/10699278
Therefore, the GCF of Fractions 64/69,80/61,72/82,164/62 is 4/10699278
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 69,61,82,62 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(69,61,82,62) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(69,61,82,62) x common factors =1 x 2 = 2
LCM(69,61,82,62) = ( 69 × 61 × 82 × 62 ) / 2
LCM(69,61,82,62) = 21398556 / 2
LCM(69,61,82,62) = 10699278
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 64/69, 80/61, 72/82, 164/62?
Answer: GCF of Numerators as per given numbers 64/69, 80/61, 72/82, 164/62 is
GCF of Numerators i.e. for 64,80,72,164 is 4
LCM of denominators i.e. for 69,61,82,62 is 10699278.
Thus, GCF of Fractions is 4/10699278.Finally, GCF of Fractions for 64/69, 80/61, 72/82, 164/62 is 4/10699278.