Use our free GCF of Fractions Calculator tool to compute the GCF of 71/58, 37/48, 874/16 i.e 1/1392 easily. The following is the detailed procedure to determine the greatest common factor of fractions 71/58, 37/48, 874/16.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 71/58,37/48,874/16
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 71/58,37/48,874/16, numerators are 71,37,874
Denominators are 58,48,16
The GCF of 71,37,874 is 1 .
LCM of 58,48,16 is 1392.
The greatest common factor of 71/58,37/48,874/16 = [GCF of 71,37,874]/[LCM of 58,48,16]= 1/1392
Therefore, the GCF of 71/58,37/48,874/16 is 1/1392.
To find the highest common factor of 71,37,874, we have to find the factors of both numbers and list the highest common factor.
The factors of 71 are 1, 71
The factors of 37 are 1, 37
The factors of 874 are 1, 2, 19, 23, 38, 46, 437, 874
The HCF of 71,37,874 is 1.
Lets's calculate GCF of 71,37,874
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 71
:1,71
Now, list down the factors of 37
:1,37
Now, list down the factors of 874
:1,2,19,23,38,46,437,874
Greatest Common Factor
We found the factors 71,37,874 . The biggest common factor number is the GCF number.
So the greatest common factor 71,37,874 is 1.
Lets's calculate LCM of 58,48,16
2 | 58, 48, 16 |
2 | 29, 24, 8 |
2 | 29, 12, 4 |
2 | 29, 6, 2 |
29, 3, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 29 x 3 x 1 = 1392
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1392
Therefore, the GCF of Fractions 71/58,37/48,874/16 is 1/1392
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 58,48,16 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(58,48,16) = 2
common factors(in case of two or more numbers have common factors) = 16
GCF(58,48,16) x common factors =2 x 16 = 32
LCM(58,48,16) = ( 58 × 48 × 16 ) / 32
LCM(58,48,16) = 44544 / 32
LCM(58,48,16) = 1392
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 71,37,874?
The HCF of 71,37,874 is 1
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 71/58, 37/48, 874/16?
Answer: GCF of Numerators as per given numbers 71/58, 37/48, 874/16 is
GCF of Numerators i.e. for 71,37,874 is 1
LCM of denominators i.e. for 58,48,16 is 1392.
Thus, GCF of Fractions is 1/1392.Finally, GCF of Fractions for 71/58, 37/48, 874/16 is 1/1392.