Use our free GCF of Fractions Calculator tool to compute the GCF of 684/360, 456/513 i.e 228/20520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 684/360, 456/513.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 684/360,456/513
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 684/360,456/513, numerators are 684,456
Denominators are 360,513
The GCF of 684,456 is 228 .
LCM of 360,513 is 20520.
The greatest common factor of 684/360,456/513 = [GCF of 684,456]/[LCM of 360,513]= 228/20520
Therefore, the GCF of 684/360,456/513 is 228/20520.
To find the highest common factor of 684,456, we have to find the factors of both numbers and list the highest common factor.
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
The HCF of 684,456 is 228.
Lets's calculate GCF of 684,456
2 | 684, 456 |
2 | 342, 228 |
3 | 171, 114 |
19 | 57, 38 |
3, 2 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 19 = 228
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
Now, list down the factors of 456
:1,2,3,4,6,8,12,19,24,38,57,76,114,152,228,456
Greatest Common Factor
We found the factors 684,456 . The biggest common factor number is the GCF number.
So the greatest common factor 684,456 is 228.
Lets's calculate LCM of 360,513
3 | 360, 513 |
3 | 120, 171 |
40, 57 |
∴ So the LCM of the given numbers is 3 x 3 x 40 x 57 = 20520
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 228/20520
Therefore, the GCF of Fractions 684/360,456/513 is 228/20520
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 360,513 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(360,513) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(360,513) x common factors =9 x 1 = 9
LCM(360,513) = ( 360 × 513 ) / 9
LCM(360,513) = 184680 / 9
LCM(360,513) = 20520
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 684,456?
The HCF of 684,456 is 228
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 684/360, 456/513?
Answer: GCF of Numerators as per given numbers 684/360, 456/513 is
GCF of Numerators i.e. for 684,456 is 228
LCM of denominators i.e. for 360,513 is 20520.
Thus, GCF of Fractions is 228/20520.Finally, GCF of Fractions for 684/360, 456/513 is 228/20520.