GCF of 46/40, 74/64, 14/12, 27/20
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 46/40, 74/64, 14/12, 27/20 i.e 1/960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 46/40, 74/64, 14/12, 27/20.
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 46/40,74/64,14/12,27/20?
Given fractions are 46/40,74/64,14/12,27/20
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 46/40,74/64,14/12,27/20, numerators are 46,74,14,27
Denominators are 40,64,12,20
The GCF of 46,74,14,27 is 1 .
LCM of 40,64,12,20 is 960.
The greatest common factor of 46/40,74/64,14/12,27/20 = [GCF of 46,74,14,27]/[LCM of 40,64,12,20]= 1/960
Therefore, the GCF of 46/40,74/64,14/12,27/20 is 1/960.
To find the highest common factor of 46,74,14,27, we have to find the factors of both numbers and list the highest common factor.
The factors of 46 are 1, 2, 23, 46
The factors of 74 are 1, 2, 37, 74
The factors of 14 are 1, 2, 7, 14
The factors of 27 are 1, 3, 9, 27
The HCF of 46,74,14,27 is 1.
Lets's calculate GCF of 46,74,14,27
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 46,74,14,27 By Matching Biggest Common Factor Method
Now, list down the factors of 46
:1,2,23,46
Now, list down the factors of 74
:1,2,37,74
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 27
:1,3,9,27
Greatest Common Factor
We found the factors 46,74,14,27 . The biggest common factor number is the GCF number.
So the greatest common factor 46,74,14,27 is 1.
Lets's calculate LCM of 40,64,12,20
| 2 | 40, 64, 12, 20 |
| 2 | 20, 32, 6, 10 |
| 2 | 5, 16, 3, 10 |
| 5 | 5, 8, 3, 5 |
| 1, 8, 3, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 1 x 8 x 3 x 1 = 960
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/960
Therefore, the GCF of Fractions 46/40,74/64,14/12,27/20 is 1/960
Least Common Multiple of 40,64,12,20 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 40,64,12,20 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,64,12,20) = 4
common factors(in case of two or more numbers have common factors) = 160
GCF(40,64,12,20) x common factors =4 x 160 = 640
LCM(40,64,12,20) = ( 40 × 64 × 12 × 20 ) / 640
LCM(40,64,12,20) = 614400 / 640
LCM(40,64,12,20) = 960
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 46/40, 74/64, 14/12, 27/20
1. What is the HCF of 46,74,14,27?
The HCF of 46,74,14,27 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 46/40, 74/64, 14/12, 27/20?
Answer: GCF of Numerators as per given numbers 46/40, 74/64, 14/12, 27/20 is
GCF of Numerators i.e. for 46,74,14,27 is 1
LCM of denominators i.e. for 40,64,12,20 is 960.
Thus, GCF of Fractions is 1/960.Finally, GCF of Fractions for 46/40, 74/64, 14/12, 27/20 is 1/960.