GCF of 2/30, 84/42, 14/479, 164/993
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2/30, 84/42, 14/479, 164/993 i.e 2/33295290 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2/30, 84/42, 14/479, 164/993.
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 2/30,84/42,14/479,164/993?
Given fractions are 2/30,84/42,14/479,164/993
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 2/30,84/42,14/479,164/993, numerators are 2,84,14,164
Denominators are 30,42,479,993
The GCF of 2,84,14,164 is 2 .
LCM of 30,42,479,993 is 33295290.
The greatest common factor of 2/30,84/42,14/479,164/993 = [GCF of 2,84,14,164]/[LCM of 30,42,479,993]= 2/33295290
Therefore, the GCF of 2/30,84/42,14/479,164/993 is 2/33295290.
To find the highest common factor of 2,84,14,164, we have to find the factors of both numbers and list the highest common factor.
The factors of 2 are 1, 2
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 14 are 1, 2, 7, 14
The factors of 164 are 1, 2, 4, 41, 82, 164
The HCF of 2,84,14,164 is 2.
Lets's calculate GCF of 2,84,14,164
| 2 | 2, 84, 14, 164 |
| 1, 42, 7, 82 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 2,84,14,164 By Matching Biggest Common Factor Method
Now, list down the factors of 2
:1,2
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 164
:1,2,4,41,82,164
Greatest Common Factor
We found the factors 2,84,14,164 . The biggest common factor number is the GCF number.
So the greatest common factor 2,84,14,164 is 2.
Lets's calculate LCM of 30,42,479,993
| 2 | 30, 42, 479, 993 |
| 3 | 15, 21, 479, 993 |
| 5, 7, 479, 331 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 7 x 479 x 331 = 33295290
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/33295290
Therefore, the GCF of Fractions 2/30,84/42,14/479,164/993 is 2/33295290
Least Common Multiple of 30,42,479,993 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 30,42,479,993 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,42,479,993) = 1
common factors(in case of two or more numbers have common factors) = 18
GCF(30,42,479,993) x common factors =1 x 18 = 18
LCM(30,42,479,993) = ( 30 × 42 × 479 × 993 ) / 18
LCM(30,42,479,993) = 599315220 / 18
LCM(30,42,479,993) = 33295290
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 2/30, 84/42, 14/479, 164/993
1. What is the HCF of 2,84,14,164?
The HCF of 2,84,14,164 is 2
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 2/30, 84/42, 14/479, 164/993?
Answer: GCF of Numerators as per given numbers 2/30, 84/42, 14/479, 164/993 is
GCF of Numerators i.e. for 2,84,14,164 is 2
LCM of denominators i.e. for 30,42,479,993 is 33295290.
Thus, GCF of Fractions is 2/33295290.Finally, GCF of Fractions for 2/30, 84/42, 14/479, 164/993 is 2/33295290.