Use our free GCF of Fractions Calculator tool to compute the GCF of 553/514, 406/153 i.e 7/78642 easily. The following is the detailed procedure to determine the greatest common factor of fractions 553/514, 406/153.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 553/514,406/153
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 553/514,406/153, numerators are 553,406
Denominators are 514,153
The GCF of 553,406 is 7 .
LCM of 514,153 is 78642.
The greatest common factor of 553/514,406/153 = [GCF of 553,406]/[LCM of 514,153]= 7/78642
Therefore, the GCF of 553/514,406/153 is 7/78642.
To find the highest common factor of 553,406, we have to find the factors of both numbers and list the highest common factor.
The factors of 553 are 1, 7, 79, 553
The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406
The HCF of 553,406 is 7.
Lets's calculate GCF of 553,406
7 | 553, 406 |
79, 58 |
∴ So the GCF of the given numbers is 7 = 7
Now, list down the factors of 553
:1,7,79,553
Now, list down the factors of 406
:1,2,7,14,29,58,203,406
Greatest Common Factor
We found the factors 553,406 . The biggest common factor number is the GCF number.
So the greatest common factor 553,406 is 7.
Lets's calculate LCM of 514,153
Given numbers has no common factors except 1. So, there LCM is their product i.e 78642
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/78642
Therefore, the GCF of Fractions 553/514,406/153 is 7/78642
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 514,153 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(514,153) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(514,153) x common factors =1 x 1 = 1
LCM(514,153) = ( 514 × 153 ) / 1
LCM(514,153) = 78642 / 1
LCM(514,153) = 78642
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 553,406?
The HCF of 553,406 is 7
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 553/514, 406/153?
Answer: GCF of Numerators as per given numbers 553/514, 406/153 is
GCF of Numerators i.e. for 553,406 is 7
LCM of denominators i.e. for 514,153 is 78642.
Thus, GCF of Fractions is 7/78642.Finally, GCF of Fractions for 553/514, 406/153 is 7/78642.