Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 27/69,73/72,82/36,632/74
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 27,73,82,632
Greatest Common Factor of Numerators i.e. GCF of 27,73,82,632 is 1 .
LCM of Denominators means LCM of 69,72,36,74 as per the given fractions.
LCM of 69,72,36,74 is 61272 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 27,73,82,632
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 27
List of positive integer factors of 27 that divides 27 without a remainder.
1,3,9,27
Factors of 73
List of positive integer factors of 73 that divides 73 without a remainder.
1,73
Factors of 82
List of positive integer factors of 82 that divides 82 without a remainder.
1,2,41,82
Factors of 632
List of positive integer factors of 632 that divides 632 without a remainder.
1,2,4,8,79,158,316,632
Greatest Common Factor
We found the factors 27,73,82,632 . The biggest common factor number is the GCF number.
So the greatest common factor 27,73,82,632 is 1.
Lets's calculate LCM of 69,72,36,74
2 | 69, 72, 36, 74 |
2 | 69, 36, 18, 37 |
3 | 69, 9, 18, 37 |
3 | 23, 3, 6, 37 |
23, 1, 2, 37 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 23 x 1 x 2 x 37 = 61272
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/61272
Therefore, the GCF of Fractions 27/69,73/72,82/36,632/74 is 1/61272
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 69,72,36,74 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(69,72,36,74) = 1
common factors(in case of two or more numbers have common factors) = 216
GCF(69,72,36,74) x common factors =1 x 216 = 216
LCM(69,72,36,74) = ( 69 × 72 × 36 × 74 ) / 216
LCM(69,72,36,74) = 13234752 / 216
LCM(69,72,36,74) = 61272
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 27/69, 73/72, 82/36, 632/74?
Answer: GCF of Numerators as per given numbers 27/69, 73/72, 82/36, 632/74 is
GCF of Numerators i.e. for 27,73,82,632 is 1
LCM of denominators i.e. for 69,72,36,74 is 61272.
Thus, GCF of Fractions is 1/61272.Finally, GCF of Fractions for 27/69, 73/72, 82/36, 632/74 is 1/61272.