Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 414/68,508/21,156/75
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 414,508,156
Greatest Common Factor of Numerators i.e. GCF of 414,508,156 is 2 .
LCM of Denominators means LCM of 68,21,75 as per the given fractions.
LCM of 68,21,75 is 35700 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 414,508,156
2 | 414, 508, 156 |
207, 254, 78 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 414
List of positive integer factors of 414 that divides 414 without a remainder.
1,2,3,6,9,18,23,46,69,138,207,414
Factors of 508
List of positive integer factors of 508 that divides 508 without a remainder.
1,2,4,127,254,508
Factors of 156
List of positive integer factors of 156 that divides 156 without a remainder.
1,2,3,4,6,12,13,26,39,52,78,156
Greatest Common Factor
We found the factors 414,508,156 . The biggest common factor number is the GCF number.
So the greatest common factor 414,508,156 is 2.
Lets's calculate LCM of 68,21,75
3 | 68, 21, 75 |
68, 7, 25 |
∴ So the LCM of the given numbers is 3 x 68 x 7 x 25 = 35700
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/35700
Therefore, the GCF of Fractions 414/68,508/21,156/75 is 2/35700
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 68,21,75 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(68,21,75) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(68,21,75) x common factors =1 x 3 = 3
LCM(68,21,75) = ( 68 × 21 × 75 ) / 3
LCM(68,21,75) = 107100 / 3
LCM(68,21,75) = 35700
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 414/68, 508/21, 156/75?
Answer: GCF of Numerators as per given numbers 414/68, 508/21, 156/75 is
GCF of Numerators i.e. for 414,508,156 is 2
LCM of denominators i.e. for 68,21,75 is 35700.
Thus, GCF of Fractions is 2/35700.Finally, GCF of Fractions for 414/68, 508/21, 156/75 is 2/35700.