GCF of 387/354, 702/120
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 387/354, 702/120 i.e 9/7080 easily. The following is the detailed procedure to determine the greatest common factor of fractions 387/354, 702/120.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 387/354,702/120?
Given fractions are 387/354,702/120
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 387/354,702/120, numerators are 387,702
Denominators are 354,120
The GCF of 387,702 is 9 .
LCM of 354,120 is 7080.
The greatest common factor of 387/354,702/120 = [GCF of 387,702]/[LCM of 354,120]= 9/7080
Therefore, the GCF of 387/354,702/120 is 9/7080.
To find the highest common factor of 387,702, we have to find the factors of both numbers and list the highest common factor.
The factors of 387 are 1, 3, 9, 43, 129, 387
The factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702
The HCF of 387,702 is 9.
Lets's calculate GCF of 387,702
| 3 | 387, 702 |
| 3 | 129, 234 |
| 43, 78 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 387,702 By Matching Biggest Common Factor Method
Now, list down the factors of 387
:1,3,9,43,129,387
Now, list down the factors of 702
:1,2,3,6,9,13,18,26,27,39,54,78,117,234,351,702
Greatest Common Factor
We found the factors 387,702 . The biggest common factor number is the GCF number.
So the greatest common factor 387,702 is 9.
Lets's calculate LCM of 354,120
| 2 | 354, 120 |
| 3 | 177, 60 |
| 59, 20 |
∴ So the LCM of the given numbers is 2 x 3 x 59 x 20 = 7080
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/7080
Therefore, the GCF of Fractions 387/354,702/120 is 9/7080
Least Common Multiple of 354,120 with GCF Formula
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 354,120 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(354,120) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(354,120) x common factors =6 x 1 = 6
LCM(354,120) = ( 354 × 120 ) / 6
LCM(354,120) = 42480 / 6
LCM(354,120) = 7080
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FAQs on GCF of Fractions of 387/354, 702/120
1. What is the HCF of 387,702?
The HCF of 387,702 is 9
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 387/354, 702/120?
Answer: GCF of Numerators as per given numbers 387/354, 702/120 is
GCF of Numerators i.e. for 387,702 is 9
LCM of denominators i.e. for 354,120 is 7080.
Thus, GCF of Fractions is 9/7080.Finally, GCF of Fractions for 387/354, 702/120 is 9/7080.