Use our free GCF of Fractions Calculator tool to compute the GCF of 8738/282, 1664/4211 i.e 2/1187502 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8738/282, 1664/4211.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 8738/282,1664/4211
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 8738/282,1664/4211, numerators are 8738,1664
Denominators are 282,4211
The GCF of 8738,1664 is 2 .
LCM of 282,4211 is 1187502.
The greatest common factor of 8738/282,1664/4211 = [GCF of 8738,1664]/[LCM of 282,4211]= 2/1187502
Therefore, the GCF of 8738/282,1664/4211 is 2/1187502.
To find the highest common factor of 8738,1664, we have to find the factors of both numbers and list the highest common factor.
The factors of 8738 are 1, 2, 17, 34, 257, 514, 4369, 8738
The factors of 1664 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664
The HCF of 8738,1664 is 2.
Lets's calculate GCF of 8738,1664
2 | 8738, 1664 |
4369, 832 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 8738
:1,2,17,34,257,514,4369,8738
Now, list down the factors of 1664
:1,2,4,8,13,16,26,32,52,64,104,128,208,416,832,1664
Greatest Common Factor
We found the factors 8738,1664 . The biggest common factor number is the GCF number.
So the greatest common factor 8738,1664 is 2.
Lets's calculate LCM of 282,4211
Given numbers has no common factors except 1. So, there LCM is their product i.e 1187502
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1187502
Therefore, the GCF of Fractions 8738/282,1664/4211 is 2/1187502
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 282,4211 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(282,4211) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(282,4211) x common factors =1 x 1 = 1
LCM(282,4211) = ( 282 × 4211 ) / 1
LCM(282,4211) = 1187502 / 1
LCM(282,4211) = 1187502
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 8738,1664?
The HCF of 8738,1664 is 2
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 8738/282, 1664/4211?
Answer: GCF of Numerators as per given numbers 8738/282, 1664/4211 is
GCF of Numerators i.e. for 8738,1664 is 2
LCM of denominators i.e. for 282,4211 is 1187502.
Thus, GCF of Fractions is 2/1187502.Finally, GCF of Fractions for 8738/282, 1664/4211 is 2/1187502.