Use our free GCF of Fractions Calculator tool to compute the GCF of 975/351, 213/759 i.e 3/88803 easily. The following is the detailed procedure to determine the greatest common factor of fractions 975/351, 213/759.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 975/351,213/759
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 975/351,213/759, numerators are 975,213
Denominators are 351,759
The GCF of 975,213 is 3 .
LCM of 351,759 is 88803.
The greatest common factor of 975/351,213/759 = [GCF of 975,213]/[LCM of 351,759]= 3/88803
Therefore, the GCF of 975/351,213/759 is 3/88803.
To find the highest common factor of 975,213, we have to find the factors of both numbers and list the highest common factor.
The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
The factors of 213 are 1, 3, 71, 213
The HCF of 975,213 is 3.
Lets's calculate GCF of 975,213
3 | 975, 213 |
325, 71 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 975
:1,3,5,13,15,25,39,65,75,195,325,975
Now, list down the factors of 213
:1,3,71,213
Greatest Common Factor
We found the factors 975,213 . The biggest common factor number is the GCF number.
So the greatest common factor 975,213 is 3.
Lets's calculate LCM of 351,759
3 | 351, 759 |
117, 253 |
∴ So the LCM of the given numbers is 3 x 117 x 253 = 88803
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/88803
Therefore, the GCF of Fractions 975/351,213/759 is 3/88803
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 351,759 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(351,759) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(351,759) x common factors =3 x 1 = 3
LCM(351,759) = ( 351 × 759 ) / 3
LCM(351,759) = 266409 / 3
LCM(351,759) = 88803
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 975,213?
The HCF of 975,213 is 3
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 975/351, 213/759?
Answer: GCF of Numerators as per given numbers 975/351, 213/759 is
GCF of Numerators i.e. for 975,213 is 3
LCM of denominators i.e. for 351,759 is 88803.
Thus, GCF of Fractions is 3/88803.Finally, GCF of Fractions for 975/351, 213/759 is 3/88803.