GCF of 42/27, 31/12, 69/13, 16/91
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 42/27, 31/12, 69/13, 16/91 i.e 1/9828 easily. The following is the detailed procedure to determine the greatest common factor of fractions 42/27, 31/12, 69/13, 16/91.
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 42/27,31/12,69/13,16/91?
Given fractions are 42/27,31/12,69/13,16/91
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 42/27,31/12,69/13,16/91, numerators are 42,31,69,16
Denominators are 27,12,13,91
The GCF of 42,31,69,16 is 1 .
LCM of 27,12,13,91 is 9828.
The greatest common factor of 42/27,31/12,69/13,16/91 = [GCF of 42,31,69,16]/[LCM of 27,12,13,91]= 1/9828
Therefore, the GCF of 42/27,31/12,69/13,16/91 is 1/9828.
To find the highest common factor of 42,31,69,16, we have to find the factors of both numbers and list the highest common factor.
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 31 are 1, 31
The factors of 69 are 1, 3, 23, 69
The factors of 16 are 1, 2, 4, 8, 16
The HCF of 42,31,69,16 is 1.
Lets's calculate GCF of 42,31,69,16
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 42,31,69,16 By Matching Biggest Common Factor Method
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 31
:1,31
Now, list down the factors of 69
:1,3,23,69
Now, list down the factors of 16
:1,2,4,8,16
Greatest Common Factor
We found the factors 42,31,69,16 . The biggest common factor number is the GCF number.
So the greatest common factor 42,31,69,16 is 1.
Lets's calculate LCM of 27,12,13,91
| 3 | 27, 12, 13, 91 |
| 13 | 9, 4, 13, 91 |
| 9, 4, 1, 7 |
∴ So the LCM of the given numbers is 3 x 13 x 9 x 4 x 1 x 7 = 9828
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9828
Therefore, the GCF of Fractions 42/27,31/12,69/13,16/91 is 1/9828
Least Common Multiple of 27,12,13,91 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 27,12,13,91 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(27,12,13,91) = 1
common factors(in case of two or more numbers have common factors) = 39
GCF(27,12,13,91) x common factors =1 x 39 = 39
LCM(27,12,13,91) = ( 27 × 12 × 13 × 91 ) / 39
LCM(27,12,13,91) = 383292 / 39
LCM(27,12,13,91) = 9828
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FAQs on GCF of Fractions of 42/27, 31/12, 69/13, 16/91
1. What is the HCF of 42,31,69,16?
The HCF of 42,31,69,16 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 42/27, 31/12, 69/13, 16/91?
Answer: GCF of Numerators as per given numbers 42/27, 31/12, 69/13, 16/91 is
GCF of Numerators i.e. for 42,31,69,16 is 1
LCM of denominators i.e. for 27,12,13,91 is 9828.
Thus, GCF of Fractions is 1/9828.Finally, GCF of Fractions for 42/27, 31/12, 69/13, 16/91 is 1/9828.