Use our free GCF of Fractions Calculator tool to compute the GCF of 852/564, 748/974 i.e 4/274668 easily. The following is the detailed procedure to determine the greatest common factor of fractions 852/564, 748/974.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 852/564,748/974
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 852/564,748/974, numerators are 852,748
Denominators are 564,974
The GCF of 852,748 is 4 .
LCM of 564,974 is 274668.
The greatest common factor of 852/564,748/974 = [GCF of 852,748]/[LCM of 564,974]= 4/274668
Therefore, the GCF of 852/564,748/974 is 4/274668.
To find the highest common factor of 852,748, we have to find the factors of both numbers and list the highest common factor.
The factors of 852 are 1, 2, 3, 4, 6, 12, 71, 142, 213, 284, 426, 852
The factors of 748 are 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748
The HCF of 852,748 is 4.
Lets's calculate GCF of 852,748
2 | 852, 748 |
2 | 426, 374 |
213, 187 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 852
:1,2,3,4,6,12,71,142,213,284,426,852
Now, list down the factors of 748
:1,2,4,11,17,22,34,44,68,187,374,748
Greatest Common Factor
We found the factors 852,748 . The biggest common factor number is the GCF number.
So the greatest common factor 852,748 is 4.
Lets's calculate LCM of 564,974
2 | 564, 974 |
282, 487 |
∴ So the LCM of the given numbers is 2 x 282 x 487 = 274668
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/274668
Therefore, the GCF of Fractions 852/564,748/974 is 4/274668
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 564,974 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(564,974) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(564,974) x common factors =2 x 1 = 2
LCM(564,974) = ( 564 × 974 ) / 2
LCM(564,974) = 549336 / 2
LCM(564,974) = 274668
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 852,748?
The HCF of 852,748 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 852/564, 748/974?
Answer: GCF of Numerators as per given numbers 852/564, 748/974 is
GCF of Numerators i.e. for 852,748 is 4
LCM of denominators i.e. for 564,974 is 274668.
Thus, GCF of Fractions is 4/274668.Finally, GCF of Fractions for 852/564, 748/974 is 4/274668.