GCF of 43/28, 68/74, 20/21, 21/984
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 43/28, 68/74, 20/21, 21/984 i.e 1/254856 easily. The following is the detailed procedure to determine the greatest common factor of fractions 43/28, 68/74, 20/21, 21/984.
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 43/28,68/74,20/21,21/984?
Given fractions are 43/28,68/74,20/21,21/984
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 43/28,68/74,20/21,21/984, numerators are 43,68,20,21
Denominators are 28,74,21,984
The GCF of 43,68,20,21 is 1 .
LCM of 28,74,21,984 is 254856.
The greatest common factor of 43/28,68/74,20/21,21/984 = [GCF of 43,68,20,21]/[LCM of 28,74,21,984]= 1/254856
Therefore, the GCF of 43/28,68/74,20/21,21/984 is 1/254856.
To find the highest common factor of 43,68,20,21, we have to find the factors of both numbers and list the highest common factor.
The factors of 43 are 1, 43
The factors of 68 are 1, 2, 4, 17, 34, 68
The factors of 20 are 1, 2, 4, 5, 10, 20
The factors of 21 are 1, 3, 7, 21
The HCF of 43,68,20,21 is 1.
Lets's calculate GCF of 43,68,20,21
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 43,68,20,21 By Matching Biggest Common Factor Method
Now, list down the factors of 43
:1,43
Now, list down the factors of 68
:1,2,4,17,34,68
Now, list down the factors of 20
:1,2,4,5,10,20
Now, list down the factors of 21
:1,3,7,21
Greatest Common Factor
We found the factors 43,68,20,21 . The biggest common factor number is the GCF number.
So the greatest common factor 43,68,20,21 is 1.
Lets's calculate LCM of 28,74,21,984
| 2 | 28, 74, 21, 984 |
| 2 | 14, 37, 21, 492 |
| 3 | 7, 37, 21, 246 |
| 7 | 7, 37, 7, 82 |
| 1, 37, 1, 82 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 1 x 37 x 1 x 82 = 254856
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/254856
Therefore, the GCF of Fractions 43/28,68/74,20/21,21/984 is 1/254856
Least Common Multiple of 28,74,21,984 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 28,74,21,984 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(28,74,21,984) = 1
common factors(in case of two or more numbers have common factors) = 168
GCF(28,74,21,984) x common factors =1 x 168 = 168
LCM(28,74,21,984) = ( 28 × 74 × 21 × 984 ) / 168
LCM(28,74,21,984) = 42815808 / 168
LCM(28,74,21,984) = 254856
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 43/28, 68/74, 20/21, 21/984
1. What is the HCF of 43,68,20,21?
The HCF of 43,68,20,21 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 43/28, 68/74, 20/21, 21/984?
Answer: GCF of Numerators as per given numbers 43/28, 68/74, 20/21, 21/984 is
GCF of Numerators i.e. for 43,68,20,21 is 1
LCM of denominators i.e. for 28,74,21,984 is 254856.
Thus, GCF of Fractions is 1/254856.Finally, GCF of Fractions for 43/28, 68/74, 20/21, 21/984 is 1/254856.