Use our free GCF of Fractions Calculator tool to compute the GCF of 48/392, 36/224, 290/342 i.e 2/268128 easily. The following is the detailed procedure to determine the greatest common factor of fractions 48/392, 36/224, 290/342.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 48/392,36/224,290/342
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 48/392,36/224,290/342, numerators are 48,36,290
Denominators are 392,224,342
The GCF of 48,36,290 is 2 .
LCM of 392,224,342 is 268128.
The greatest common factor of 48/392,36/224,290/342 = [GCF of 48,36,290]/[LCM of 392,224,342]= 2/268128
Therefore, the GCF of 48/392,36/224,290/342 is 2/268128.
To find the highest common factor of 48,36,290, we have to find the factors of both numbers and list the highest common factor.
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 290 are 1, 2, 5, 10, 29, 58, 145, 290
The HCF of 48,36,290 is 2.
Lets's calculate GCF of 48,36,290
2 | 48, 36, 290 |
24, 18, 145 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 48
:1,2,3,4,6,8,12,16,24,48
Now, list down the factors of 36
:1,2,3,4,6,9,12,18,36
Now, list down the factors of 290
:1,2,5,10,29,58,145,290
Greatest Common Factor
We found the factors 48,36,290 . The biggest common factor number is the GCF number.
So the greatest common factor 48,36,290 is 2.
Lets's calculate LCM of 392,224,342
2 | 392, 224, 342 |
2 | 196, 112, 171 |
2 | 98, 56, 171 |
7 | 49, 28, 171 |
7, 4, 171 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 7 x 7 x 4 x 171 = 268128
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/268128
Therefore, the GCF of Fractions 48/392,36/224,290/342 is 2/268128
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 392,224,342 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(392,224,342) = 2
common factors(in case of two or more numbers have common factors) = 56
GCF(392,224,342) x common factors =2 x 56 = 112
LCM(392,224,342) = ( 392 × 224 × 342 ) / 112
LCM(392,224,342) = 30030336 / 112
LCM(392,224,342) = 268128
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 48,36,290?
The HCF of 48,36,290 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 48/392, 36/224, 290/342?
Answer: GCF of Numerators as per given numbers 48/392, 36/224, 290/342 is
GCF of Numerators i.e. for 48,36,290 is 2
LCM of denominators i.e. for 392,224,342 is 268128.
Thus, GCF of Fractions is 2/268128.Finally, GCF of Fractions for 48/392, 36/224, 290/342 is 2/268128.