Use our free GCF of Fractions Calculator tool to compute the GCF of 36/13, 261/22, 684/708 i.e 9/101244 easily. The following is the detailed procedure to determine the greatest common factor of fractions 36/13, 261/22, 684/708.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 36/13,261/22,684/708
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 36/13,261/22,684/708, numerators are 36,261,684
Denominators are 13,22,708
The GCF of 36,261,684 is 9 .
LCM of 13,22,708 is 101244.
The greatest common factor of 36/13,261/22,684/708 = [GCF of 36,261,684]/[LCM of 13,22,708]= 9/101244
Therefore, the GCF of 36/13,261/22,684/708 is 9/101244.
To find the highest common factor of 36,261,684, we have to find the factors of both numbers and list the highest common factor.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 261 are 1, 3, 9, 29, 87, 261
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The HCF of 36,261,684 is 9.
Lets's calculate GCF of 36,261,684
3 | 36, 261, 684 |
3 | 12, 87, 228 |
4, 29, 76 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Now, list down the factors of 36
:1,2,3,4,6,9,12,18,36
Now, list down the factors of 261
:1,3,9,29,87,261
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Greatest Common Factor
We found the factors 36,261,684 . The biggest common factor number is the GCF number.
So the greatest common factor 36,261,684 is 9.
Lets's calculate LCM of 13,22,708
2 | 13, 22, 708 |
13, 11, 354 |
∴ So the LCM of the given numbers is 2 x 13 x 11 x 354 = 101244
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/101244
Therefore, the GCF of Fractions 36/13,261/22,684/708 is 9/101244
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 13,22,708 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(13,22,708) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(13,22,708) x common factors =1 x 2 = 2
LCM(13,22,708) = ( 13 × 22 × 708 ) / 2
LCM(13,22,708) = 202488 / 2
LCM(13,22,708) = 101244
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 36,261,684?
The HCF of 36,261,684 is 9
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 36/13, 261/22, 684/708?
Answer: GCF of Numerators as per given numbers 36/13, 261/22, 684/708 is
GCF of Numerators i.e. for 36,261,684 is 9
LCM of denominators i.e. for 13,22,708 is 101244.
Thus, GCF of Fractions is 9/101244.Finally, GCF of Fractions for 36/13, 261/22, 684/708 is 9/101244.