GCF of 68/67, 40/14, 39/12, 30/24
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 68/67, 40/14, 39/12, 30/24 i.e 1/11256 easily. The following is the detailed procedure to determine the greatest common factor of fractions 68/67, 40/14, 39/12, 30/24.
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 68/67,40/14,39/12,30/24?
Given fractions are 68/67,40/14,39/12,30/24
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 68/67,40/14,39/12,30/24, numerators are 68,40,39,30
Denominators are 67,14,12,24
The GCF of 68,40,39,30 is 1 .
LCM of 67,14,12,24 is 11256.
The greatest common factor of 68/67,40/14,39/12,30/24 = [GCF of 68,40,39,30]/[LCM of 67,14,12,24]= 1/11256
Therefore, the GCF of 68/67,40/14,39/12,30/24 is 1/11256.
To find the highest common factor of 68,40,39,30, we have to find the factors of both numbers and list the highest common factor.
The factors of 68 are 1, 2, 4, 17, 34, 68
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 39 are 1, 3, 13, 39
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The HCF of 68,40,39,30 is 1.
Lets's calculate GCF of 68,40,39,30
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 68,40,39,30 By Matching Biggest Common Factor Method
Now, list down the factors of 68
:1,2,4,17,34,68
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 39
:1,3,13,39
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Greatest Common Factor
We found the factors 68,40,39,30 . The biggest common factor number is the GCF number.
So the greatest common factor 68,40,39,30 is 1.
Lets's calculate LCM of 67,14,12,24
| 2 | 67, 14, 12, 24 |
| 2 | 67, 7, 6, 12 |
| 3 | 67, 7, 3, 6 |
| 67, 7, 1, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 67 x 7 x 1 x 2 = 11256
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/11256
Therefore, the GCF of Fractions 68/67,40/14,39/12,30/24 is 1/11256
Least Common Multiple of 67,14,12,24 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 67,14,12,24 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(67,14,12,24) = 1
common factors(in case of two or more numbers have common factors) = 24
GCF(67,14,12,24) x common factors =1 x 24 = 24
LCM(67,14,12,24) = ( 67 × 14 × 12 × 24 ) / 24
LCM(67,14,12,24) = 270144 / 24
LCM(67,14,12,24) = 11256
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 68/67, 40/14, 39/12, 30/24
1. What is the HCF of 68,40,39,30?
The HCF of 68,40,39,30 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 68/67, 40/14, 39/12, 30/24?
Answer: GCF of Numerators as per given numbers 68/67, 40/14, 39/12, 30/24 is
GCF of Numerators i.e. for 68,40,39,30 is 1
LCM of denominators i.e. for 67,14,12,24 is 11256.
Thus, GCF of Fractions is 1/11256.Finally, GCF of Fractions for 68/67, 40/14, 39/12, 30/24 is 1/11256.