Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 26/77,24/42,75/32,61/84
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 26,24,75,61
Greatest Common Factor of Numerators i.e. GCF of 26,24,75,61 is 1 .
LCM of Denominators means LCM of 77,42,32,84 as per the given fractions.
LCM of 77,42,32,84 is 7392 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 26,24,75,61
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 26
List of positive integer factors of 26 that divides 26 without a remainder.
1,2,13,26
Factors of 24
List of positive integer factors of 24 that divides 24 without a remainder.
1,2,3,4,6,8,12,24
Factors of 75
List of positive integer factors of 75 that divides 75 without a remainder.
1,3,5,15,25,75
Factors of 61
List of positive integer factors of 61 that divides 61 without a remainder.
1,61
Greatest Common Factor
We found the factors 26,24,75,61 . The biggest common factor number is the GCF number.
So the greatest common factor 26,24,75,61 is 1.
Lets's calculate LCM of 77,42,32,84
2 | 77, 42, 32, 84 |
2 | 77, 21, 16, 42 |
3 | 77, 21, 8, 21 |
7 | 77, 7, 8, 7 |
11, 1, 8, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 11 x 1 x 8 x 1 = 7392
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7392
Therefore, the GCF of Fractions 26/77,24/42,75/32,61/84 is 1/7392
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 77,42,32,84 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,42,32,84) = 1
common factors(in case of two or more numbers have common factors) = 1176
GCF(77,42,32,84) x common factors =1 x 1176 = 1176
LCM(77,42,32,84) = ( 77 × 42 × 32 × 84 ) / 1176
LCM(77,42,32,84) = 8692992 / 1176
LCM(77,42,32,84) = 7392
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 26/77, 24/42, 75/32, 61/84?
Answer: GCF of Numerators as per given numbers 26/77, 24/42, 75/32, 61/84 is
GCF of Numerators i.e. for 26,24,75,61 is 1
LCM of denominators i.e. for 77,42,32,84 is 7392.
Thus, GCF of Fractions is 1/7392.Finally, GCF of Fractions for 26/77, 24/42, 75/32, 61/84 is 1/7392.