Use our free GCF of Fractions Calculator tool to compute the GCF of 402/175, 945/700 i.e 3/700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 402/175, 945/700.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 402/175,945/700
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 402/175,945/700, numerators are 402,945
Denominators are 175,700
The GCF of 402,945 is 3 .
LCM of 175,700 is 700.
The greatest common factor of 402/175,945/700 = [GCF of 402,945]/[LCM of 175,700]= 3/700
Therefore, the GCF of 402/175,945/700 is 3/700.
To find the highest common factor of 402,945, we have to find the factors of both numbers and list the highest common factor.
The factors of 402 are 1, 2, 3, 6, 67, 134, 201, 402
The factors of 945 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, 945
The HCF of 402,945 is 3.
Lets's calculate GCF of 402,945
3 | 402, 945 |
134, 315 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 402
:1,2,3,6,67,134,201,402
Now, list down the factors of 945
:1,3,5,7,9,15,21,27,35,45,63,105,135,189,315,945
Greatest Common Factor
We found the factors 402,945 . The biggest common factor number is the GCF number.
So the greatest common factor 402,945 is 3.
Lets's calculate LCM of 175,700
5 | 175, 700 |
5 | 35, 140 |
7 | 7, 28 |
1, 4 |
∴ So the LCM of the given numbers is 5 x 5 x 7 x 1 x 4 = 700
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/700
Therefore, the GCF of Fractions 402/175,945/700 is 3/700
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 175,700 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(175,700) = 175
common factors(in case of two or more numbers have common factors) = 1
GCF(175,700) x common factors =175 x 1 = 175
LCM(175,700) = ( 175 × 700 ) / 175
LCM(175,700) = 122500 / 175
LCM(175,700) = 700
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 402,945?
The HCF of 402,945 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 402/175, 945/700?
Answer: GCF of Numerators as per given numbers 402/175, 945/700 is
GCF of Numerators i.e. for 402,945 is 3
LCM of denominators i.e. for 175,700 is 700.
Thus, GCF of Fractions is 3/700.Finally, GCF of Fractions for 402/175, 945/700 is 3/700.