Use our free GCF of Fractions Calculator tool to compute the GCF of 840/35, 460/2814 i.e 20/14070 easily. The following is the detailed procedure to determine the greatest common factor of fractions 840/35, 460/2814.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 840/35,460/2814
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 840/35,460/2814, numerators are 840,460
Denominators are 35,2814
The GCF of 840,460 is 20 .
LCM of 35,2814 is 14070.
The greatest common factor of 840/35,460/2814 = [GCF of 840,460]/[LCM of 35,2814]= 20/14070
Therefore, the GCF of 840/35,460/2814 is 20/14070.
To find the highest common factor of 840,460, we have to find the factors of both numbers and list the highest common factor.
The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
The factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460
The HCF of 840,460 is 20.
Lets's calculate GCF of 840,460
2 | 840, 460 |
2 | 420, 230 |
5 | 210, 115 |
42, 23 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Now, list down the factors of 840
:1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,28,30,35,40,42,56,60,70,84,105,120,140,168,210,280,420,840
Now, list down the factors of 460
:1,2,4,5,10,20,23,46,92,115,230,460
Greatest Common Factor
We found the factors 840,460 . The biggest common factor number is the GCF number.
So the greatest common factor 840,460 is 20.
Lets's calculate LCM of 35,2814
7 | 35, 2814 |
5, 402 |
∴ So the LCM of the given numbers is 7 x 5 x 402 = 14070
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/14070
Therefore, the GCF of Fractions 840/35,460/2814 is 20/14070
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 35,2814 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(35,2814) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(35,2814) x common factors =7 x 1 = 7
LCM(35,2814) = ( 35 × 2814 ) / 7
LCM(35,2814) = 98490 / 7
LCM(35,2814) = 14070
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 840,460?
The HCF of 840,460 is 20
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 840/35, 460/2814?
Answer: GCF of Numerators as per given numbers 840/35, 460/2814 is
GCF of Numerators i.e. for 840,460 is 20
LCM of denominators i.e. for 35,2814 is 14070.
Thus, GCF of Fractions is 20/14070.Finally, GCF of Fractions for 840/35, 460/2814 is 20/14070.