Use our free GCF of Fractions Calculator tool to compute the GCF of 420/550, 350/904 i.e 70/248600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 420/550, 350/904.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 420/550,350/904
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 420/550,350/904, numerators are 420,350
Denominators are 550,904
The GCF of 420,350 is 70 .
LCM of 550,904 is 248600.
The greatest common factor of 420/550,350/904 = [GCF of 420,350]/[LCM of 550,904]= 70/248600
Therefore, the GCF of 420/550,350/904 is 70/248600.
To find the highest common factor of 420,350, we have to find the factors of both numbers and list the highest common factor.
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350
The HCF of 420,350 is 70.
Lets's calculate GCF of 420,350
2 | 420, 350 |
5 | 210, 175 |
7 | 42, 35 |
6, 5 |
∴ So the GCF of the given numbers is 2 x 5 x 7 = 70
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Now, list down the factors of 350
:1,2,5,7,10,14,25,35,50,70,175,350
Greatest Common Factor
We found the factors 420,350 . The biggest common factor number is the GCF number.
So the greatest common factor 420,350 is 70.
Lets's calculate LCM of 550,904
2 | 550, 904 |
275, 452 |
∴ So the LCM of the given numbers is 2 x 275 x 452 = 248600
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 70/248600
Therefore, the GCF of Fractions 420/550,350/904 is 70/248600
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 550,904 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(550,904) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(550,904) x common factors =2 x 1 = 2
LCM(550,904) = ( 550 × 904 ) / 2
LCM(550,904) = 497200 / 2
LCM(550,904) = 248600
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 420,350?
The HCF of 420,350 is 70
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 420/550, 350/904?
Answer: GCF of Numerators as per given numbers 420/550, 350/904 is
GCF of Numerators i.e. for 420,350 is 70
LCM of denominators i.e. for 550,904 is 248600.
Thus, GCF of Fractions is 70/248600.Finally, GCF of Fractions for 420/550, 350/904 is 70/248600.