Use our free GCF of Fractions Calculator tool to compute the GCF of 50/108, 42/812, 280/609 i.e 2/21924 easily. The following is the detailed procedure to determine the greatest common factor of fractions 50/108, 42/812, 280/609.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 50/108,42/812,280/609
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 50/108,42/812,280/609, numerators are 50,42,280
Denominators are 108,812,609
The GCF of 50,42,280 is 2 .
LCM of 108,812,609 is 21924.
The greatest common factor of 50/108,42/812,280/609 = [GCF of 50,42,280]/[LCM of 108,812,609]= 2/21924
Therefore, the GCF of 50/108,42/812,280/609 is 2/21924.
To find the highest common factor of 50,42,280, we have to find the factors of both numbers and list the highest common factor.
The factors of 50 are 1, 2, 5, 10, 25, 50
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280
The HCF of 50,42,280 is 2.
Lets's calculate GCF of 50,42,280
2 | 50, 42, 280 |
25, 21, 140 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 50
:1,2,5,10,25,50
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 280
:1,2,4,5,7,8,10,14,20,28,35,40,56,70,140,280
Greatest Common Factor
We found the factors 50,42,280 . The biggest common factor number is the GCF number.
So the greatest common factor 50,42,280 is 2.
Lets's calculate LCM of 108,812,609
2 | 108, 812, 609 |
2 | 54, 406, 609 |
3 | 27, 203, 609 |
7 | 9, 203, 203 |
29 | 9, 29, 29 |
9, 1, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 29 x 9 x 1 x 1 = 21924
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/21924
Therefore, the GCF of Fractions 50/108,42/812,280/609 is 2/21924
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 108,812,609 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(108,812,609) = 1
common factors(in case of two or more numbers have common factors) = 2436
GCF(108,812,609) x common factors =1 x 2436 = 2436
LCM(108,812,609) = ( 108 × 812 × 609 ) / 2436
LCM(108,812,609) = 53406864 / 2436
LCM(108,812,609) = 21924
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 50,42,280?
The HCF of 50,42,280 is 2
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. 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.
4. What is the GCF of Fractions for 50/108, 42/812, 280/609?
Answer: GCF of Numerators as per given numbers 50/108, 42/812, 280/609 is
GCF of Numerators i.e. for 50,42,280 is 2
LCM of denominators i.e. for 108,812,609 is 21924.
Thus, GCF of Fractions is 2/21924.Finally, GCF of Fractions for 50/108, 42/812, 280/609 is 2/21924.