GCF of 16/40, 49/20, 76/12, 77/27
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 16/40, 49/20, 76/12, 77/27 i.e 1/1080 easily. The following is the detailed procedure to determine the greatest common factor of fractions 16/40, 49/20, 76/12, 77/27.
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 16/40,49/20,76/12,77/27?
Given fractions are 16/40,49/20,76/12,77/27
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 16/40,49/20,76/12,77/27, numerators are 16,49,76,77
Denominators are 40,20,12,27
The GCF of 16,49,76,77 is 1 .
LCM of 40,20,12,27 is 1080.
The greatest common factor of 16/40,49/20,76/12,77/27 = [GCF of 16,49,76,77]/[LCM of 40,20,12,27]= 1/1080
Therefore, the GCF of 16/40,49/20,76/12,77/27 is 1/1080.
To find the highest common factor of 16,49,76,77, 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 49 are 1, 7, 49
The factors of 76 are 1, 2, 4, 19, 38, 76
The factors of 77 are 1, 7, 11, 77
The HCF of 16,49,76,77 is 1.
Lets's calculate GCF of 16,49,76,77
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 16,49,76,77 By Matching Biggest Common Factor Method
Now, list down the factors of 16
:1,2,4,8,16
Now, list down the factors of 49
:1,7,49
Now, list down the factors of 76
:1,2,4,19,38,76
Now, list down the factors of 77
:1,7,11,77
Greatest Common Factor
We found the factors 16,49,76,77 . The biggest common factor number is the GCF number.
So the greatest common factor 16,49,76,77 is 1.
Lets's calculate LCM of 40,20,12,27
| 2 | 40, 20, 12, 27 |
| 2 | 20, 10, 6, 27 |
| 3 | 5, 10, 3, 27 |
| 5 | 5, 10, 1, 9 |
| 1, 2, 1, 9 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 1 x 2 x 1 x 9 = 1080
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1080
Therefore, the GCF of Fractions 16/40,49/20,76/12,77/27 is 1/1080
Least Common Multiple of 40,20,12,27 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 40,20,12,27 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,20,12,27) = 1
common factors(in case of two or more numbers have common factors) = 240
GCF(40,20,12,27) x common factors =1 x 240 = 240
LCM(40,20,12,27) = ( 40 × 20 × 12 × 27 ) / 240
LCM(40,20,12,27) = 259200 / 240
LCM(40,20,12,27) = 1080
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 16/40, 49/20, 76/12, 77/27
1. What is the HCF of 16,49,76,77?
The HCF of 16,49,76,77 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 16/40, 49/20, 76/12, 77/27?
Answer: GCF of Numerators as per given numbers 16/40, 49/20, 76/12, 77/27 is
GCF of Numerators i.e. for 16,49,76,77 is 1
LCM of denominators i.e. for 40,20,12,27 is 1080.
Thus, GCF of Fractions is 1/1080.Finally, GCF of Fractions for 16/40, 49/20, 76/12, 77/27 is 1/1080.