GCF of 21/70, 13/80, 94/78, 96/14
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 21/70, 13/80, 94/78, 96/14 i.e 1/21840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/70, 13/80, 94/78, 96/14.
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 21/70,13/80,94/78,96/14?
Given fractions are 21/70,13/80,94/78,96/14
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 21/70,13/80,94/78,96/14, numerators are 21,13,94,96
Denominators are 70,80,78,14
The GCF of 21,13,94,96 is 1 .
LCM of 70,80,78,14 is 21840.
The greatest common factor of 21/70,13/80,94/78,96/14 = [GCF of 21,13,94,96]/[LCM of 70,80,78,14]= 1/21840
Therefore, the GCF of 21/70,13/80,94/78,96/14 is 1/21840.
To find the highest common factor of 21,13,94,96, we have to find the factors of both numbers and list the highest common factor.
The factors of 21 are 1, 3, 7, 21
The factors of 13 are 1, 13
The factors of 94 are 1, 2, 47, 94
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The HCF of 21,13,94,96 is 1.
Lets's calculate GCF of 21,13,94,96
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 21,13,94,96 By Matching Biggest Common Factor Method
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 13
:1,13
Now, list down the factors of 94
:1,2,47,94
Now, list down the factors of 96
:1,2,3,4,6,8,12,16,24,32,48,96
Greatest Common Factor
We found the factors 21,13,94,96 . The biggest common factor number is the GCF number.
So the greatest common factor 21,13,94,96 is 1.
Lets's calculate LCM of 70,80,78,14
| 2 | 70, 80, 78, 14 |
| 5 | 35, 40, 39, 7 |
| 7 | 7, 8, 39, 7 |
| 1, 8, 39, 1 |
∴ So the LCM of the given numbers is 2 x 5 x 7 x 1 x 8 x 39 x 1 = 21840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/21840
Therefore, the GCF of Fractions 21/70,13/80,94/78,96/14 is 1/21840
Least Common Multiple of 70,80,78,14 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 70,80,78,14 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(70,80,78,14) = 2
common factors(in case of two or more numbers have common factors) = 140
GCF(70,80,78,14) x common factors =2 x 140 = 280
LCM(70,80,78,14) = ( 70 × 80 × 78 × 14 ) / 280
LCM(70,80,78,14) = 6115200 / 280
LCM(70,80,78,14) = 21840
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 21/70, 13/80, 94/78, 96/14
1. What is the HCF of 21,13,94,96?
The HCF of 21,13,94,96 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 21/70, 13/80, 94/78, 96/14?
Answer: GCF of Numerators as per given numbers 21/70, 13/80, 94/78, 96/14 is
GCF of Numerators i.e. for 21,13,94,96 is 1
LCM of denominators i.e. for 70,80,78,14 is 21840.
Thus, GCF of Fractions is 1/21840.Finally, GCF of Fractions for 21/70, 13/80, 94/78, 96/14 is 1/21840.