GCF of 14/49, 67/98, 80/24, 17/20
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 14/49, 67/98, 80/24, 17/20 i.e 1/5880 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/49, 67/98, 80/24, 17/20.
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 14/49,67/98,80/24,17/20?
Given fractions are 14/49,67/98,80/24,17/20
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 14/49,67/98,80/24,17/20, numerators are 14,67,80,17
Denominators are 49,98,24,20
The GCF of 14,67,80,17 is 1 .
LCM of 49,98,24,20 is 5880.
The greatest common factor of 14/49,67/98,80/24,17/20 = [GCF of 14,67,80,17]/[LCM of 49,98,24,20]= 1/5880
Therefore, the GCF of 14/49,67/98,80/24,17/20 is 1/5880.
To find the highest common factor of 14,67,80,17, we have to find the factors of both numbers and list the highest common factor.
The factors of 14 are 1, 2, 7, 14
The factors of 67 are 1, 67
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
The factors of 17 are 1, 17
The HCF of 14,67,80,17 is 1.
Lets's calculate GCF of 14,67,80,17
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 14,67,80,17 By Matching Biggest Common Factor Method
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 67
:1,67
Now, list down the factors of 80
:1,2,4,5,8,10,16,20,40,80
Now, list down the factors of 17
:1,17
Greatest Common Factor
We found the factors 14,67,80,17 . The biggest common factor number is the GCF number.
So the greatest common factor 14,67,80,17 is 1.
Lets's calculate LCM of 49,98,24,20
| 2 | 49, 98, 24, 20 |
| 2 | 49, 49, 12, 10 |
| 7 | 49, 49, 6, 5 |
| 7 | 7, 7, 6, 5 |
| 1, 1, 6, 5 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 7 x 1 x 1 x 6 x 5 = 5880
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5880
Therefore, the GCF of Fractions 14/49,67/98,80/24,17/20 is 1/5880
Least Common Multiple of 49,98,24,20 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 49,98,24,20 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(49,98,24,20) = 1
common factors(in case of two or more numbers have common factors) = 392
GCF(49,98,24,20) x common factors =1 x 392 = 392
LCM(49,98,24,20) = ( 49 × 98 × 24 × 20 ) / 392
LCM(49,98,24,20) = 2304960 / 392
LCM(49,98,24,20) = 5880
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 14/49, 67/98, 80/24, 17/20
1. What is the HCF of 14,67,80,17?
The HCF of 14,67,80,17 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 14/49, 67/98, 80/24, 17/20?
Answer: GCF of Numerators as per given numbers 14/49, 67/98, 80/24, 17/20 is
GCF of Numerators i.e. for 14,67,80,17 is 1
LCM of denominators i.e. for 49,98,24,20 is 5880.
Thus, GCF of Fractions is 1/5880.Finally, GCF of Fractions for 14/49, 67/98, 80/24, 17/20 is 1/5880.