Use our free GCF of Fractions Calculator tool to compute the GCF of 780/754, 132/335 i.e 12/252590 easily. The following is the detailed procedure to determine the greatest common factor of fractions 780/754, 132/335.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 780/754,132/335
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 780/754,132/335, numerators are 780,132
Denominators are 754,335
The GCF of 780,132 is 12 .
LCM of 754,335 is 252590.
The greatest common factor of 780/754,132/335 = [GCF of 780,132]/[LCM of 754,335]= 12/252590
Therefore, the GCF of 780/754,132/335 is 12/252590.
To find the highest common factor of 780,132, we have to find the factors of both numbers and list the highest common factor.
The factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780
The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
The HCF of 780,132 is 12.
Lets's calculate GCF of 780,132
2 | 780, 132 |
2 | 390, 66 |
3 | 195, 33 |
65, 11 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Now, list down the factors of 780
:1,2,3,4,5,6,10,12,13,15,20,26,30,39,52,60,65,78,130,156,195,260,390,780
Now, list down the factors of 132
:1,2,3,4,6,11,12,22,33,44,66,132
Greatest Common Factor
We found the factors 780,132 . The biggest common factor number is the GCF number.
So the greatest common factor 780,132 is 12.
Lets's calculate LCM of 754,335
Given numbers has no common factors except 1. So, there LCM is their product i.e 252590
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/252590
Therefore, the GCF of Fractions 780/754,132/335 is 12/252590
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 754,335 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(754,335) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(754,335) x common factors =1 x 1 = 1
LCM(754,335) = ( 754 × 335 ) / 1
LCM(754,335) = 252590 / 1
LCM(754,335) = 252590
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 780,132?
The HCF of 780,132 is 12
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 780/754, 132/335?
Answer: GCF of Numerators as per given numbers 780/754, 132/335 is
GCF of Numerators i.e. for 780,132 is 12
LCM of denominators i.e. for 754,335 is 252590.
Thus, GCF of Fractions is 12/252590.Finally, GCF of Fractions for 780/754, 132/335 is 12/252590.