Use our free GCF of Fractions Calculator tool to compute the GCF of 469/421, 420/513 i.e 7/215973 easily. The following is the detailed procedure to determine the greatest common factor of fractions 469/421, 420/513.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 469/421,420/513
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 469/421,420/513, numerators are 469,420
Denominators are 421,513
The GCF of 469,420 is 7 .
LCM of 421,513 is 215973.
The greatest common factor of 469/421,420/513 = [GCF of 469,420]/[LCM of 421,513]= 7/215973
Therefore, the GCF of 469/421,420/513 is 7/215973.
To find the highest common factor of 469,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 469 are 1, 7, 67, 469
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 469,420 is 7.
Lets's calculate GCF of 469,420
7 | 469, 420 |
67, 60 |
∴ So the GCF of the given numbers is 7 = 7
Now, list down the factors of 469
:1,7,67,469
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 469,420 . The biggest common factor number is the GCF number.
So the greatest common factor 469,420 is 7.
Lets's calculate LCM of 421,513
Given numbers has no common factors except 1. So, there LCM is their product i.e 215973
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/215973
Therefore, the GCF of Fractions 469/421,420/513 is 7/215973
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 421,513 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(421,513) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(421,513) x common factors =1 x 1 = 1
LCM(421,513) = ( 421 × 513 ) / 1
LCM(421,513) = 215973 / 1
LCM(421,513) = 215973
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 469,420?
The HCF of 469,420 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 469/421, 420/513?
Answer: GCF of Numerators as per given numbers 469/421, 420/513 is
GCF of Numerators i.e. for 469,420 is 7
LCM of denominators i.e. for 421,513 is 215973.
Thus, GCF of Fractions is 7/215973.Finally, GCF of Fractions for 469/421, 420/513 is 7/215973.