Use our free GCF of Fractions Calculator tool to compute the GCF of 156/147, 120/105 i.e 12/735 easily. The following is the detailed procedure to determine the greatest common factor of fractions 156/147, 120/105.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 156/147,120/105
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 156/147,120/105, numerators are 156,120
Denominators are 147,105
The GCF of 156,120 is 12 .
LCM of 147,105 is 735.
The greatest common factor of 156/147,120/105 = [GCF of 156,120]/[LCM of 147,105]= 12/735
Therefore, the GCF of 156/147,120/105 is 12/735.
To find the highest common factor of 156,120, we have to find the factors of both numbers and list the highest common factor.
The factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The HCF of 156,120 is 12.
Lets's calculate GCF of 156,120
2 | 156, 120 |
2 | 78, 60 |
3 | 39, 30 |
13, 10 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Now, list down the factors of 156
:1,2,3,4,6,12,13,26,39,52,78,156
Now, list down the factors of 120
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Greatest Common Factor
We found the factors 156,120 . The biggest common factor number is the GCF number.
So the greatest common factor 156,120 is 12.
Lets's calculate LCM of 147,105
3 | 147, 105 |
7 | 49, 35 |
7, 5 |
∴ So the LCM of the given numbers is 3 x 7 x 7 x 5 = 735
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/735
Therefore, the GCF of Fractions 156/147,120/105 is 12/735
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 147,105 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(147,105) = 21
common factors(in case of two or more numbers have common factors) = 1
GCF(147,105) x common factors =21 x 1 = 21
LCM(147,105) = ( 147 × 105 ) / 21
LCM(147,105) = 15435 / 21
LCM(147,105) = 735
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 156,120?
The HCF of 156,120 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 156/147, 120/105?
Answer: GCF of Numerators as per given numbers 156/147, 120/105 is
GCF of Numerators i.e. for 156,120 is 12
LCM of denominators i.e. for 147,105 is 735.
Thus, GCF of Fractions is 12/735.Finally, GCF of Fractions for 156/147, 120/105 is 12/735.