GCF of 414/51, 378/984
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 414/51, 378/984 i.e 18/16728 easily. The following is the detailed procedure to determine the greatest common factor of fractions 414/51, 378/984.
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 414/51,378/984?
Given fractions are 414/51,378/984
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 414/51,378/984, numerators are 414,378
Denominators are 51,984
The GCF of 414,378 is 18 .
LCM of 51,984 is 16728.
The greatest common factor of 414/51,378/984 = [GCF of 414,378]/[LCM of 51,984]= 18/16728
Therefore, the GCF of 414/51,378/984 is 18/16728.
To find the highest common factor of 414,378, we have to find the factors of both numbers and list the highest common factor.
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The HCF of 414,378 is 18.
Lets's calculate GCF of 414,378
| 2 | 414, 378 |
| 3 | 207, 189 |
| 3 | 69, 63 |
| 23, 21 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 414,378 By Matching Biggest Common Factor Method
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Now, list down the factors of 378
:1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Greatest Common Factor
We found the factors 414,378 . The biggest common factor number is the GCF number.
So the greatest common factor 414,378 is 18.
Lets's calculate LCM of 51,984
| 3 | 51, 984 |
| 17, 328 |
∴ So the LCM of the given numbers is 3 x 17 x 328 = 16728
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/16728
Therefore, the GCF of Fractions 414/51,378/984 is 18/16728
Least Common Multiple of 51,984 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 51,984 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,984) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(51,984) x common factors =3 x 1 = 3
LCM(51,984) = ( 51 × 984 ) / 3
LCM(51,984) = 50184 / 3
LCM(51,984) = 16728
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 414/51, 378/984
1. What is the HCF of 414,378?
The HCF of 414,378 is 18
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 414/51, 378/984?
Answer: GCF of Numerators as per given numbers 414/51, 378/984 is
GCF of Numerators i.e. for 414,378 is 18
LCM of denominators i.e. for 51,984 is 16728.
Thus, GCF of Fractions is 18/16728.Finally, GCF of Fractions for 414/51, 378/984 is 18/16728.