GCF of 399/21, 308/7182
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 399/21, 308/7182 i.e 7/7182 easily. The following is the detailed procedure to determine the greatest common factor of fractions 399/21, 308/7182.
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 399/21,308/7182?
Given fractions are 399/21,308/7182
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 399/21,308/7182, numerators are 399,308
Denominators are 21,7182
The GCF of 399,308 is 7 .
LCM of 21,7182 is 7182.
The greatest common factor of 399/21,308/7182 = [GCF of 399,308]/[LCM of 21,7182]= 7/7182
Therefore, the GCF of 399/21,308/7182 is 7/7182.
To find the highest common factor of 399,308, we have to find the factors of both numbers and list the highest common factor.
The factors of 399 are 1, 3, 7, 19, 21, 57, 133, 399
The factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308
The HCF of 399,308 is 7.
Lets's calculate GCF of 399,308
| 7 | 399, 308 |
| 57, 44 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 399,308 By Matching Biggest Common Factor Method
Now, list down the factors of 399
:1,3,7,19,21,57,133,399
Now, list down the factors of 308
:1,2,4,7,11,14,22,28,44,77,154,308
Greatest Common Factor
We found the factors 399,308 . The biggest common factor number is the GCF number.
So the greatest common factor 399,308 is 7.
Lets's calculate LCM of 21,7182
| 3 | 21, 7182 |
| 7 | 7, 2394 |
| 1, 342 |
∴ So the LCM of the given numbers is 3 x 7 x 1 x 342 = 7182
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/7182
Therefore, the GCF of Fractions 399/21,308/7182 is 7/7182
Least Common Multiple of 21,7182 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 21,7182 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,7182) = 21
common factors(in case of two or more numbers have common factors) = 1
GCF(21,7182) x common factors =21 x 1 = 21
LCM(21,7182) = ( 21 × 7182 ) / 21
LCM(21,7182) = 150822 / 21
LCM(21,7182) = 7182
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FAQs on GCF of Fractions of 399/21, 308/7182
1. What is the HCF of 399,308?
The HCF of 399,308 is 7
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 399/21, 308/7182?
Answer: GCF of Numerators as per given numbers 399/21, 308/7182 is
GCF of Numerators i.e. for 399,308 is 7
LCM of denominators i.e. for 21,7182 is 7182.
Thus, GCF of Fractions is 7/7182.Finally, GCF of Fractions for 399/21, 308/7182 is 7/7182.