Use our free GCF of Fractions Calculator tool to compute the GCF of 64/29, 284/49, 900/105 i.e 4/21315 easily. The following is the detailed procedure to determine the greatest common factor of fractions 64/29, 284/49, 900/105.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 64/29,284/49,900/105
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 64/29,284/49,900/105, numerators are 64,284,900
Denominators are 29,49,105
The GCF of 64,284,900 is 4 .
LCM of 29,49,105 is 21315.
The greatest common factor of 64/29,284/49,900/105 = [GCF of 64,284,900]/[LCM of 29,49,105]= 4/21315
Therefore, the GCF of 64/29,284/49,900/105 is 4/21315.
To find the highest common factor of 64,284,900, we have to find the factors of both numbers and list the highest common factor.
The factors of 64 are 1, 2, 4, 8, 16, 32, 64
The factors of 284 are 1, 2, 4, 71, 142, 284
The factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900
The HCF of 64,284,900 is 4.
Lets's calculate GCF of 64,284,900
2 | 64, 284, 900 |
2 | 32, 142, 450 |
16, 71, 225 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 64
:1,2,4,8,16,32,64
Now, list down the factors of 284
:1,2,4,71,142,284
Now, list down the factors of 900
:1,2,3,4,5,6,9,10,12,15,18,20,25,30,36,45,50,60,75,90,100,150,180,225,300,450,900
Greatest Common Factor
We found the factors 64,284,900 . The biggest common factor number is the GCF number.
So the greatest common factor 64,284,900 is 4.
Lets's calculate LCM of 29,49,105
7 | 29, 49, 105 |
29, 7, 15 |
∴ So the LCM of the given numbers is 7 x 29 x 7 x 15 = 21315
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/21315
Therefore, the GCF of Fractions 64/29,284/49,900/105 is 4/21315
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 29,49,105 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(29,49,105) = 1
common factors(in case of two or more numbers have common factors) = 7
GCF(29,49,105) x common factors =1 x 7 = 7
LCM(29,49,105) = ( 29 × 49 × 105 ) / 7
LCM(29,49,105) = 149205 / 7
LCM(29,49,105) = 21315
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 64,284,900?
The HCF of 64,284,900 is 4
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 64/29, 284/49, 900/105?
Answer: GCF of Numerators as per given numbers 64/29, 284/49, 900/105 is
GCF of Numerators i.e. for 64,284,900 is 4
LCM of denominators i.e. for 29,49,105 is 21315.
Thus, GCF of Fractions is 4/21315.Finally, GCF of Fractions for 64/29, 284/49, 900/105 is 4/21315.