GCF of 49/12, 40/52, 85/75, 78/27
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 49/12, 40/52, 85/75, 78/27 i.e 1/35100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 49/12, 40/52, 85/75, 78/27.
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 49/12,40/52,85/75,78/27?
Given fractions are 49/12,40/52,85/75,78/27
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 49/12,40/52,85/75,78/27, numerators are 49,40,85,78
Denominators are 12,52,75,27
The GCF of 49,40,85,78 is 1 .
LCM of 12,52,75,27 is 35100.
The greatest common factor of 49/12,40/52,85/75,78/27 = [GCF of 49,40,85,78]/[LCM of 12,52,75,27]= 1/35100
Therefore, the GCF of 49/12,40/52,85/75,78/27 is 1/35100.
To find the highest common factor of 49,40,85,78, we have to find the factors of both numbers and list the highest common factor.
The factors of 49 are 1, 7, 49
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 85 are 1, 5, 17, 85
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
The HCF of 49,40,85,78 is 1.
Lets's calculate GCF of 49,40,85,78
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 49,40,85,78 By Matching Biggest Common Factor Method
Now, list down the factors of 49
:1,7,49
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 85
:1,5,17,85
Now, list down the factors of 78
:1,2,3,6,13,26,39,78
Greatest Common Factor
We found the factors 49,40,85,78 . The biggest common factor number is the GCF number.
So the greatest common factor 49,40,85,78 is 1.
Lets's calculate LCM of 12,52,75,27
| 2 | 12, 52, 75, 27 |
| 2 | 6, 26, 75, 27 |
| 3 | 3, 13, 75, 27 |
| 1, 13, 25, 9 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 1 x 13 x 25 x 9 = 35100
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/35100
Therefore, the GCF of Fractions 49/12,40/52,85/75,78/27 is 1/35100
Least Common Multiple of 12,52,75,27 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 12,52,75,27 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,52,75,27) = 1
common factors(in case of two or more numbers have common factors) = 36
GCF(12,52,75,27) x common factors =1 x 36 = 36
LCM(12,52,75,27) = ( 12 × 52 × 75 × 27 ) / 36
LCM(12,52,75,27) = 1263600 / 36
LCM(12,52,75,27) = 35100
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FAQs on GCF of Fractions of 49/12, 40/52, 85/75, 78/27
1. What is the HCF of 49,40,85,78?
The HCF of 49,40,85,78 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 49/12, 40/52, 85/75, 78/27?
Answer: GCF of Numerators as per given numbers 49/12, 40/52, 85/75, 78/27 is
GCF of Numerators i.e. for 49,40,85,78 is 1
LCM of denominators i.e. for 12,52,75,27 is 35100.
Thus, GCF of Fractions is 1/35100.Finally, GCF of Fractions for 49/12, 40/52, 85/75, 78/27 is 1/35100.