GCF of 378/206, 8694/355
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 378/206, 8694/355 i.e 378/73130 easily. The following is the detailed procedure to determine the greatest common factor of fractions 378/206, 8694/355.
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 378/206,8694/355?
Given fractions are 378/206,8694/355
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 378/206,8694/355, numerators are 378,8694
Denominators are 206,355
The GCF of 378,8694 is 378 .
LCM of 206,355 is 73130.
The greatest common factor of 378/206,8694/355 = [GCF of 378,8694]/[LCM of 206,355]= 378/73130
Therefore, the GCF of 378/206,8694/355 is 378/73130.
To find the highest common factor of 378,8694, we have to find the factors of both numbers and list the highest common factor.
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The factors of 8694 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 23, 27, 42, 46, 54, 63, 69, 126, 138, 161, 189, 207, 322, 378, 414, 483, 621, 966, 1242, 1449, 2898, 4347, 8694
The HCF of 378,8694 is 378.
Lets's calculate GCF of 378,8694
| 2 | 378, 8694 |
| 3 | 189, 4347 |
| 3 | 63, 1449 |
| 3 | 21, 483 |
| 7 | 7, 161 |
| 1, 23 |
∴ So the GCF of the given numbers is 2 x 3 x 3 x 3 x 7 = 378
Greatest Common Factor of 378,8694 By Matching Biggest Common Factor Method
Now, list down the factors of 378
:1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Now, list down the factors of 8694
:1,2,3,6,7,9,14,18,21,23,27,42,46,54,63,69,126,138,161,189,207,322,378,414,483,621,966,1242,1449,2898,4347,8694
Greatest Common Factor
We found the factors 378,8694 . The biggest common factor number is the GCF number.
So the greatest common factor 378,8694 is 378.
Lets's calculate LCM of 206,355
Given numbers has no common factors except 1. So, there LCM is their product i.e 73130
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 378/73130
Therefore, the GCF of Fractions 378/206,8694/355 is 378/73130
Least Common Multiple of 206,355 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 206,355 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(206,355) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(206,355) x common factors =1 x 1 = 1
LCM(206,355) = ( 206 × 355 ) / 1
LCM(206,355) = 73130 / 1
LCM(206,355) = 73130
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FAQs on GCF of Fractions of 378/206, 8694/355
1. What is the HCF of 378,8694?
The HCF of 378,8694 is 378
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 378/206, 8694/355?
Answer: GCF of Numerators as per given numbers 378/206, 8694/355 is
GCF of Numerators i.e. for 378,8694 is 378
LCM of denominators i.e. for 206,355 is 73130.
Thus, GCF of Fractions is 378/73130.Finally, GCF of Fractions for 378/206, 8694/355 is 378/73130.