Use our free GCF of Fractions Calculator tool to compute the GCF of 516/841, 312/874 i.e 12/735034 easily. The following is the detailed procedure to determine the greatest common factor of fractions 516/841, 312/874.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 516/841,312/874
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 516/841,312/874, numerators are 516,312
Denominators are 841,874
The GCF of 516,312 is 12 .
LCM of 841,874 is 735034.
The greatest common factor of 516/841,312/874 = [GCF of 516,312]/[LCM of 841,874]= 12/735034
Therefore, the GCF of 516/841,312/874 is 12/735034.
To find the highest common factor of 516,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 516 are 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 516,312 is 12.
Lets's calculate GCF of 516,312
2 | 516, 312 |
2 | 258, 156 |
3 | 129, 78 |
43, 26 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Now, list down the factors of 516
:1,2,3,4,6,12,43,86,129,172,258,516
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 516,312 . The biggest common factor number is the GCF number.
So the greatest common factor 516,312 is 12.
Lets's calculate LCM of 841,874
Given numbers has no common factors except 1. So, there LCM is their product i.e 735034
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/735034
Therefore, the GCF of Fractions 516/841,312/874 is 12/735034
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 841,874 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(841,874) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(841,874) x common factors =1 x 1 = 1
LCM(841,874) = ( 841 × 874 ) / 1
LCM(841,874) = 735034 / 1
LCM(841,874) = 735034
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 516,312?
The HCF of 516,312 is 12
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 516/841, 312/874?
Answer: GCF of Numerators as per given numbers 516/841, 312/874 is
GCF of Numerators i.e. for 516,312 is 12
LCM of denominators i.e. for 841,874 is 735034.
Thus, GCF of Fractions is 12/735034.Finally, GCF of Fractions for 516/841, 312/874 is 12/735034.