GCF of 378/210, 669/684
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 378/210, 669/684 i.e 3/23940 easily. The following is the detailed procedure to determine the greatest common factor of fractions 378/210, 669/684.
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 378/210,669/684?
Given fractions are 378/210,669/684
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 378/210,669/684, numerators are 378,669
Denominators are 210,684
The GCF of 378,669 is 3 .
LCM of 210,684 is 23940.
The greatest common factor of 378/210,669/684 = [GCF of 378,669]/[LCM of 210,684]= 3/23940
Therefore, the GCF of 378/210,669/684 is 3/23940.
To find the highest common factor of 378,669, 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 669 are 1, 3, 223, 669
The HCF of 378,669 is 3.
Lets's calculate GCF of 378,669
| 3 | 378, 669 |
| 126, 223 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 378,669 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 669
:1,3,223,669
Greatest Common Factor
We found the factors 378,669 . The biggest common factor number is the GCF number.
So the greatest common factor 378,669 is 3.
Lets's calculate LCM of 210,684
| 2 | 210, 684 |
| 3 | 105, 342 |
| 35, 114 |
∴ So the LCM of the given numbers is 2 x 3 x 35 x 114 = 23940
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/23940
Therefore, the GCF of Fractions 378/210,669/684 is 3/23940
Least Common Multiple of 210,684 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 210,684 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(210,684) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(210,684) x common factors =6 x 1 = 6
LCM(210,684) = ( 210 × 684 ) / 6
LCM(210,684) = 143640 / 6
LCM(210,684) = 23940
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FAQs on GCF of Fractions of 378/210, 669/684
1. What is the HCF of 378,669?
The HCF of 378,669 is 3
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 378/210, 669/684?
Answer: GCF of Numerators as per given numbers 378/210, 669/684 is
GCF of Numerators i.e. for 378,669 is 3
LCM of denominators i.e. for 210,684 is 23940.
Thus, GCF of Fractions is 3/23940.Finally, GCF of Fractions for 378/210, 669/684 is 3/23940.