GCF of 88/25, 31/74, 74/43, 40/20
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 88/25, 31/74, 74/43, 40/20 i.e 1/159100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 88/25, 31/74, 74/43, 40/20.
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 88/25,31/74,74/43,40/20?
Given fractions are 88/25,31/74,74/43,40/20
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 88/25,31/74,74/43,40/20, numerators are 88,31,74,40
Denominators are 25,74,43,20
The GCF of 88,31,74,40 is 1 .
LCM of 25,74,43,20 is 159100.
The greatest common factor of 88/25,31/74,74/43,40/20 = [GCF of 88,31,74,40]/[LCM of 25,74,43,20]= 1/159100
Therefore, the GCF of 88/25,31/74,74/43,40/20 is 1/159100.
To find the highest common factor of 88,31,74,40, we have to find the factors of both numbers and list the highest common factor.
The factors of 88 are 1, 2, 4, 8, 11, 22, 44, 88
The factors of 31 are 1, 31
The factors of 74 are 1, 2, 37, 74
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The HCF of 88,31,74,40 is 1.
Lets's calculate GCF of 88,31,74,40
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 88,31,74,40 By Matching Biggest Common Factor Method
Now, list down the factors of 88
:1,2,4,8,11,22,44,88
Now, list down the factors of 31
:1,31
Now, list down the factors of 74
:1,2,37,74
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Greatest Common Factor
We found the factors 88,31,74,40 . The biggest common factor number is the GCF number.
So the greatest common factor 88,31,74,40 is 1.
Lets's calculate LCM of 25,74,43,20
| 2 | 25, 74, 43, 20 |
| 5 | 25, 37, 43, 10 |
| 5, 37, 43, 2 |
∴ So the LCM of the given numbers is 2 x 5 x 5 x 37 x 43 x 2 = 159100
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/159100
Therefore, the GCF of Fractions 88/25,31/74,74/43,40/20 is 1/159100
Least Common Multiple of 25,74,43,20 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 25,74,43,20 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(25,74,43,20) = 1
common factors(in case of two or more numbers have common factors) = 10
GCF(25,74,43,20) x common factors =1 x 10 = 10
LCM(25,74,43,20) = ( 25 × 74 × 43 × 20 ) / 10
LCM(25,74,43,20) = 1591000 / 10
LCM(25,74,43,20) = 159100
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FAQs on GCF of Fractions of 88/25, 31/74, 74/43, 40/20
1. What is the HCF of 88,31,74,40?
The HCF of 88,31,74,40 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 88/25, 31/74, 74/43, 40/20?
Answer: GCF of Numerators as per given numbers 88/25, 31/74, 74/43, 40/20 is
GCF of Numerators i.e. for 88,31,74,40 is 1
LCM of denominators i.e. for 25,74,43,20 is 159100.
Thus, GCF of Fractions is 1/159100.Finally, GCF of Fractions for 88/25, 31/74, 74/43, 40/20 is 1/159100.