Use our free GCF of Fractions Calculator tool to compute the GCF of 51/434, 49/1506 i.e 1/326802 easily. The following is the detailed procedure to determine the greatest common factor of fractions 51/434, 49/1506.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 51/434,49/1506
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 51/434,49/1506, numerators are 51,49
Denominators are 434,1506
The GCF of 51,49 is 1 .
LCM of 434,1506 is 326802.
The greatest common factor of 51/434,49/1506 = [GCF of 51,49]/[LCM of 434,1506]= 1/326802
Therefore, the GCF of 51/434,49/1506 is 1/326802.
To find the highest common factor of 51,49, we have to find the factors of both numbers and list the highest common factor.
The factors of 51 are 1, 3, 17, 51
The factors of 49 are 1, 7, 49
The HCF of 51,49 is 1.
Lets's calculate GCF of 51,49
∴ So GCF of numbers is 1 because of no common factors present between them.
Lets's calculate LCM of 434,1506
2 | 434, 1506 |
217, 753 |
∴ So the LCM of the given numbers is 2 x 217 x 753 = 326802
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/326802
Therefore, the GCF of Fractions 51/434,49/1506 is 1/326802
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 434,1506 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(434,1506) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(434,1506) x common factors =2 x 1 = 2
LCM(434,1506) = ( 434 × 1506 ) / 2
LCM(434,1506) = 653604 / 2
LCM(434,1506) = 326802
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 51,49?
The HCF of 51,49 is 1
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 51/434, 49/1506?
Answer: GCF of Numerators as per given numbers 51/434, 49/1506 is
GCF of Numerators i.e. for 51,49 is 1
LCM of denominators i.e. for 434,1506 is 326802.
Thus, GCF of Fractions is 1/326802.Finally, GCF of Fractions for 51/434, 49/1506 is 1/326802.