GCF of 16/42, 84/67, 82/38, 66/60
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 16/42, 84/67, 82/38, 66/60 i.e 2/534660 easily. The following is the detailed procedure to determine the greatest common factor of fractions 16/42, 84/67, 82/38, 66/60.
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 16/42,84/67,82/38,66/60?
Given fractions are 16/42,84/67,82/38,66/60
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 16/42,84/67,82/38,66/60, numerators are 16,84,82,66
Denominators are 42,67,38,60
The GCF of 16,84,82,66 is 2 .
LCM of 42,67,38,60 is 534660.
The greatest common factor of 16/42,84/67,82/38,66/60 = [GCF of 16,84,82,66]/[LCM of 42,67,38,60]= 2/534660
Therefore, the GCF of 16/42,84/67,82/38,66/60 is 2/534660.
To find the highest common factor of 16,84,82,66, we have to find the factors of both numbers and list the highest common factor.
The factors of 16 are 1, 2, 4, 8, 16
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 82 are 1, 2, 41, 82
The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66
The HCF of 16,84,82,66 is 2.
Lets's calculate GCF of 16,84,82,66
| 2 | 16, 84, 82, 66 |
| 8, 42, 41, 33 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 16,84,82,66 By Matching Biggest Common Factor Method
Now, list down the factors of 16
:1,2,4,8,16
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 82
:1,2,41,82
Now, list down the factors of 66
:1,2,3,6,11,22,33,66
Greatest Common Factor
We found the factors 16,84,82,66 . The biggest common factor number is the GCF number.
So the greatest common factor 16,84,82,66 is 2.
Lets's calculate LCM of 42,67,38,60
| 2 | 42, 67, 38, 60 |
| 3 | 21, 67, 19, 30 |
| 7, 67, 19, 10 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 67 x 19 x 10 = 534660
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/534660
Therefore, the GCF of Fractions 16/42,84/67,82/38,66/60 is 2/534660
Least Common Multiple of 42,67,38,60 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 42,67,38,60 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,67,38,60) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(42,67,38,60) x common factors =1 x 12 = 12
LCM(42,67,38,60) = ( 42 × 67 × 38 × 60 ) / 12
LCM(42,67,38,60) = 6415920 / 12
LCM(42,67,38,60) = 534660
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 16/42, 84/67, 82/38, 66/60
1. What is the HCF of 16,84,82,66?
The HCF of 16,84,82,66 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 16/42, 84/67, 82/38, 66/60?
Answer: GCF of Numerators as per given numbers 16/42, 84/67, 82/38, 66/60 is
GCF of Numerators i.e. for 16,84,82,66 is 2
LCM of denominators i.e. for 42,67,38,60 is 534660.
Thus, GCF of Fractions is 2/534660.Finally, GCF of Fractions for 16/42, 84/67, 82/38, 66/60 is 2/534660.