Use our free GCF of Fractions Calculator tool to compute the GCF of 840/723, 294/732 i.e 42/176412 easily. The following is the detailed procedure to determine the greatest common factor of fractions 840/723, 294/732.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 840/723,294/732
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 840/723,294/732, numerators are 840,294
Denominators are 723,732
The GCF of 840,294 is 42 .
LCM of 723,732 is 176412.
The greatest common factor of 840/723,294/732 = [GCF of 840,294]/[LCM of 723,732]= 42/176412
Therefore, the GCF of 840/723,294/732 is 42/176412.
To find the highest common factor of 840,294, 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 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
The HCF of 840,294 is 42.
Lets's calculate GCF of 840,294
2 | 840, 294 |
3 | 420, 147 |
7 | 140, 49 |
20, 7 |
∴ So the GCF of the given numbers is 2 x 3 x 7 = 42
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 294
:1,2,3,6,7,14,21,42,49,98,147,294
Greatest Common Factor
We found the factors 840,294 . The biggest common factor number is the GCF number.
So the greatest common factor 840,294 is 42.
Lets's calculate LCM of 723,732
3 | 723, 732 |
241, 244 |
∴ So the LCM of the given numbers is 3 x 241 x 244 = 176412
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 42/176412
Therefore, the GCF of Fractions 840/723,294/732 is 42/176412
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 723,732 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(723,732) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(723,732) x common factors =3 x 1 = 3
LCM(723,732) = ( 723 × 732 ) / 3
LCM(723,732) = 529236 / 3
LCM(723,732) = 176412
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 840,294?
The HCF of 840,294 is 42
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 840/723, 294/732?
Answer: GCF of Numerators as per given numbers 840/723, 294/732 is
GCF of Numerators i.e. for 840,294 is 42
LCM of denominators i.e. for 723,732 is 176412.
Thus, GCF of Fractions is 42/176412.Finally, GCF of Fractions for 840/723, 294/732 is 42/176412.