GCF of 60/12, 36/25, 76/20, 86/14
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 60/12, 36/25, 76/20, 86/14 i.e 2/2100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 60/12, 36/25, 76/20, 86/14.
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 60/12,36/25,76/20,86/14?
Given fractions are 60/12,36/25,76/20,86/14
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 60/12,36/25,76/20,86/14, numerators are 60,36,76,86
Denominators are 12,25,20,14
The GCF of 60,36,76,86 is 2 .
LCM of 12,25,20,14 is 2100.
The greatest common factor of 60/12,36/25,76/20,86/14 = [GCF of 60,36,76,86]/[LCM of 12,25,20,14]= 2/2100
Therefore, the GCF of 60/12,36/25,76/20,86/14 is 2/2100.
To find the highest common factor of 60,36,76,86, we have to find the factors of both numbers and list the highest common factor.
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 76 are 1, 2, 4, 19, 38, 76
The factors of 86 are 1, 2, 43, 86
The HCF of 60,36,76,86 is 2.
Lets's calculate GCF of 60,36,76,86
| 2 | 60, 36, 76, 86 |
| 30, 18, 38, 43 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 60,36,76,86 By Matching Biggest Common Factor Method
Now, list down the factors of 60
:1,2,3,4,5,6,10,12,15,20,30,60
Now, list down the factors of 36
:1,2,3,4,6,9,12,18,36
Now, list down the factors of 76
:1,2,4,19,38,76
Now, list down the factors of 86
:1,2,43,86
Greatest Common Factor
We found the factors 60,36,76,86 . The biggest common factor number is the GCF number.
So the greatest common factor 60,36,76,86 is 2.
Lets's calculate LCM of 12,25,20,14
| 2 | 12, 25, 20, 14 |
| 2 | 6, 25, 10, 7 |
| 5 | 3, 25, 5, 7 |
| 3, 1, 5, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 3 x 1 x 5 x 7 = 2100
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2100
Therefore, the GCF of Fractions 60/12,36/25,76/20,86/14 is 2/2100
Least Common Multiple of 12,25,20,14 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 12,25,20,14 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,25,20,14) = 1
common factors(in case of two or more numbers have common factors) = 40
GCF(12,25,20,14) x common factors =1 x 40 = 40
LCM(12,25,20,14) = ( 12 × 25 × 20 × 14 ) / 40
LCM(12,25,20,14) = 84000 / 40
LCM(12,25,20,14) = 2100
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 60/12, 36/25, 76/20, 86/14
1. What is the HCF of 60,36,76,86?
The HCF of 60,36,76,86 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 60/12, 36/25, 76/20, 86/14?
Answer: GCF of Numerators as per given numbers 60/12, 36/25, 76/20, 86/14 is
GCF of Numerators i.e. for 60,36,76,86 is 2
LCM of denominators i.e. for 12,25,20,14 is 2100.
Thus, GCF of Fractions is 2/2100.Finally, GCF of Fractions for 60/12, 36/25, 76/20, 86/14 is 2/2100.