Use our free GCF of Fractions Calculator tool to compute the GCF of 645/658, 312/960 i.e 3/315840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 645/658, 312/960.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 645/658,312/960
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 645/658,312/960, numerators are 645,312
Denominators are 658,960
The GCF of 645,312 is 3 .
LCM of 658,960 is 315840.
The greatest common factor of 645/658,312/960 = [GCF of 645,312]/[LCM of 658,960]= 3/315840
Therefore, the GCF of 645/658,312/960 is 3/315840.
To find the highest common factor of 645,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 645 are 1, 3, 5, 15, 43, 129, 215, 645
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 645,312 is 3.
Lets's calculate GCF of 645,312
3 | 645, 312 |
215, 104 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 645
:1,3,5,15,43,129,215,645
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 645,312 . The biggest common factor number is the GCF number.
So the greatest common factor 645,312 is 3.
Lets's calculate LCM of 658,960
2 | 658, 960 |
329, 480 |
∴ So the LCM of the given numbers is 2 x 329 x 480 = 315840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/315840
Therefore, the GCF of Fractions 645/658,312/960 is 3/315840
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 658,960 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(658,960) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(658,960) x common factors =2 x 1 = 2
LCM(658,960) = ( 658 × 960 ) / 2
LCM(658,960) = 631680 / 2
LCM(658,960) = 315840
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 645,312?
The HCF of 645,312 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 645/658, 312/960?
Answer: GCF of Numerators as per given numbers 645/658, 312/960 is
GCF of Numerators i.e. for 645,312 is 3
LCM of denominators i.e. for 658,960 is 315840.
Thus, GCF of Fractions is 3/315840.Finally, GCF of Fractions for 645/658, 312/960 is 3/315840.