GCF of 44/34, 75/85, 823/40
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 44/34, 75/85, 823/40 i.e 1/680 easily. The following is the detailed procedure to determine the greatest common factor of fractions 44/34, 75/85, 823/40.
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 44/34,75/85,823/40?
Given fractions are 44/34,75/85,823/40
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 44/34,75/85,823/40, numerators are 44,75,823
Denominators are 34,85,40
The GCF of 44,75,823 is 1 .
LCM of 34,85,40 is 680.
The greatest common factor of 44/34,75/85,823/40 = [GCF of 44,75,823]/[LCM of 34,85,40]= 1/680
Therefore, the GCF of 44/34,75/85,823/40 is 1/680.
To find the highest common factor of 44,75,823, we have to find the factors of both numbers and list the highest common factor.
The factors of 44 are 1, 2, 4, 11, 22, 44
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 823 are 1, 823
The HCF of 44,75,823 is 1.
Lets's calculate GCF of 44,75,823
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 44,75,823 By Matching Biggest Common Factor Method
Now, list down the factors of 44
:1,2,4,11,22,44
Now, list down the factors of 75
:1,3,5,15,25,75
Now, list down the factors of 823
:1,823
Greatest Common Factor
We found the factors 44,75,823 . The biggest common factor number is the GCF number.
So the greatest common factor 44,75,823 is 1.
Lets's calculate LCM of 34,85,40
| 2 | 34, 85, 40 |
| 5 | 17, 85, 20 |
| 17 | 17, 17, 4 |
| 1, 1, 4 |
∴ So the LCM of the given numbers is 2 x 5 x 17 x 1 x 1 x 4 = 680
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/680
Therefore, the GCF of Fractions 44/34,75/85,823/40 is 1/680
Least Common Multiple of 34,85,40 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 34,85,40 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,85,40) = 1
common factors(in case of two or more numbers have common factors) = 170
GCF(34,85,40) x common factors =1 x 170 = 170
LCM(34,85,40) = ( 34 × 85 × 40 ) / 170
LCM(34,85,40) = 115600 / 170
LCM(34,85,40) = 680
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FAQs on GCF of Fractions of 44/34, 75/85, 823/40
1. What is the HCF of 44,75,823?
The HCF of 44,75,823 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 44/34, 75/85, 823/40?
Answer: GCF of Numerators as per given numbers 44/34, 75/85, 823/40 is
GCF of Numerators i.e. for 44,75,823 is 1
LCM of denominators i.e. for 34,85,40 is 680.
Thus, GCF of Fractions is 1/680.Finally, GCF of Fractions for 44/34, 75/85, 823/40 is 1/680.