GCF of 20/42, 56/49, 80/51, 16/49
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 20/42, 56/49, 80/51, 16/49 i.e 4/4998 easily. The following is the detailed procedure to determine the greatest common factor of fractions 20/42, 56/49, 80/51, 16/49.
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 20/42,56/49,80/51,16/49?
Given fractions are 20/42,56/49,80/51,16/49
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 20/42,56/49,80/51,16/49, numerators are 20,56,80,16
Denominators are 42,49,51,49
The GCF of 20,56,80,16 is 4 .
LCM of 42,49,51,49 is 4998.
The greatest common factor of 20/42,56/49,80/51,16/49 = [GCF of 20,56,80,16]/[LCM of 42,49,51,49]= 4/4998
Therefore, the GCF of 20/42,56/49,80/51,16/49 is 4/4998.
To find the highest common factor of 20,56,80,16, we have to find the factors of both numbers and list the highest common factor.
The factors of 20 are 1, 2, 4, 5, 10, 20
The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
The factors of 16 are 1, 2, 4, 8, 16
The HCF of 20,56,80,16 is 4.
Lets's calculate GCF of 20,56,80,16
| 2 | 20, 56, 80, 16 |
| 2 | 10, 28, 40, 8 |
| 5, 14, 20, 4 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 20,56,80,16 By Matching Biggest Common Factor Method
Now, list down the factors of 20
:1,2,4,5,10,20
Now, list down the factors of 56
:1,2,4,7,8,14,28,56
Now, list down the factors of 80
:1,2,4,5,8,10,16,20,40,80
Now, list down the factors of 16
:1,2,4,8,16
Greatest Common Factor
We found the factors 20,56,80,16 . The biggest common factor number is the GCF number.
So the greatest common factor 20,56,80,16 is 4.
Lets's calculate LCM of 42,49,51,49
| 3 | 42, 49, 51, 49 |
| 7 | 14, 49, 17, 49 |
| 7 | 2, 7, 17, 7 |
| 2, 1, 17, 1 |
∴ So the LCM of the given numbers is 3 x 7 x 7 x 2 x 1 x 17 x 1 = 4998
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/4998
Therefore, the GCF of Fractions 20/42,56/49,80/51,16/49 is 4/4998
Least Common Multiple of 42,49,51,49 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 42,49,51,49 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,49,51,49) = 1
common factors(in case of two or more numbers have common factors) = 1029
GCF(42,49,51,49) x common factors =1 x 1029 = 1029
LCM(42,49,51,49) = ( 42 × 49 × 51 × 49 ) / 1029
LCM(42,49,51,49) = 5142942 / 1029
LCM(42,49,51,49) = 4998
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 20/42, 56/49, 80/51, 16/49
1. What is the HCF of 20,56,80,16?
The HCF of 20,56,80,16 is 4
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 20/42, 56/49, 80/51, 16/49?
Answer: GCF of Numerators as per given numbers 20/42, 56/49, 80/51, 16/49 is
GCF of Numerators i.e. for 20,56,80,16 is 4
LCM of denominators i.e. for 42,49,51,49 is 4998.
Thus, GCF of Fractions is 4/4998.Finally, GCF of Fractions for 20/42, 56/49, 80/51, 16/49 is 4/4998.