GCF of 3/21, 1/69, 6/16, 14/208
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3/21, 1/69, 6/16, 14/208 i.e 1/100464 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3/21, 1/69, 6/16, 14/208.
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 3/21,1/69,6/16,14/208?
Given fractions are 3/21,1/69,6/16,14/208
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 3/21,1/69,6/16,14/208, numerators are 3,1,6,14
Denominators are 21,69,16,208
The GCF of 3,1,6,14 is 1 .
LCM of 21,69,16,208 is 100464.
The greatest common factor of 3/21,1/69,6/16,14/208 = [GCF of 3,1,6,14]/[LCM of 21,69,16,208]= 1/100464
Therefore, the GCF of 3/21,1/69,6/16,14/208 is 1/100464.
To find the highest common factor of 3,1,6,14, we have to find the factors of both numbers and list the highest common factor.
The factors of 3 are 1, 3
The factors of 1 are 1
The factors of 6 are 1, 2, 3, 6
The factors of 14 are 1, 2, 7, 14
The HCF of 3,1,6,14 is 1.
Lets's calculate GCF of 3,1,6,14
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 3,1,6,14 By Matching Biggest Common Factor Method
Now, list down the factors of 3
:1,3
Now, list down the factors of 1
:1
Now, list down the factors of 6
:1,2,3,6
Now, list down the factors of 14
:1,2,7,14
Greatest Common Factor
We found the factors 3,1,6,14 . The biggest common factor number is the GCF number.
So the greatest common factor 3,1,6,14 is 1.
Lets's calculate LCM of 21,69,16,208
| 2 | 21, 69, 16, 208 |
| 2 | 21, 69, 8, 104 |
| 2 | 21, 69, 4, 52 |
| 2 | 21, 69, 2, 26 |
| 3 | 21, 69, 1, 13 |
| 7, 23, 1, 13 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 3 x 7 x 23 x 1 x 13 = 100464
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/100464
Therefore, the GCF of Fractions 3/21,1/69,6/16,14/208 is 1/100464
Least Common Multiple of 21,69,16,208 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 21,69,16,208 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,69,16,208) = 1
common factors(in case of two or more numbers have common factors) = 48
GCF(21,69,16,208) x common factors =1 x 48 = 48
LCM(21,69,16,208) = ( 21 × 69 × 16 × 208 ) / 48
LCM(21,69,16,208) = 4822272 / 48
LCM(21,69,16,208) = 100464
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 3/21, 1/69, 6/16, 14/208
1. What is the HCF of 3,1,6,14?
The HCF of 3,1,6,14 is 1
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 3/21, 1/69, 6/16, 14/208?
Answer: GCF of Numerators as per given numbers 3/21, 1/69, 6/16, 14/208 is
GCF of Numerators i.e. for 3,1,6,14 is 1
LCM of denominators i.e. for 21,69,16,208 is 100464.
Thus, GCF of Fractions is 1/100464.Finally, GCF of Fractions for 3/21, 1/69, 6/16, 14/208 is 1/100464.