Use our free GCF of Fractions Calculator tool to compute the GCF of 842/300, 840/912 i.e 2/22800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 842/300, 840/912.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 842/300,840/912
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 842/300,840/912, numerators are 842,840
Denominators are 300,912
The GCF of 842,840 is 2 .
LCM of 300,912 is 22800.
The greatest common factor of 842/300,840/912 = [GCF of 842,840]/[LCM of 300,912]= 2/22800
Therefore, the GCF of 842/300,840/912 is 2/22800.
To find the highest common factor of 842,840, we have to find the factors of both numbers and list the highest common factor.
The factors of 842 are 1, 2, 421, 842
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 HCF of 842,840 is 2.
Lets's calculate GCF of 842,840
2 | 842, 840 |
421, 420 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 842
:1,2,421,842
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
Greatest Common Factor
We found the factors 842,840 . The biggest common factor number is the GCF number.
So the greatest common factor 842,840 is 2.
Lets's calculate LCM of 300,912
2 | 300, 912 |
2 | 150, 456 |
3 | 75, 228 |
25, 76 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 25 x 76 = 22800
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/22800
Therefore, the GCF of Fractions 842/300,840/912 is 2/22800
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 300,912 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(300,912) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(300,912) x common factors =12 x 1 = 12
LCM(300,912) = ( 300 × 912 ) / 12
LCM(300,912) = 273600 / 12
LCM(300,912) = 22800
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 842,840?
The HCF of 842,840 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 842/300, 840/912?
Answer: GCF of Numerators as per given numbers 842/300, 840/912 is
GCF of Numerators i.e. for 842,840 is 2
LCM of denominators i.e. for 300,912 is 22800.
Thus, GCF of Fractions is 2/22800.Finally, GCF of Fractions for 842/300, 840/912 is 2/22800.