GCF of 3/31, 774/23, 438/21
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3/31, 774/23, 438/21 i.e 3/14973 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3/31, 774/23, 438/21.
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 3/31,774/23,438/21?
Given fractions are 3/31,774/23,438/21
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 3/31,774/23,438/21, numerators are 3,774,438
Denominators are 31,23,21
The GCF of 3,774,438 is 3 .
LCM of 31,23,21 is 14973.
The greatest common factor of 3/31,774/23,438/21 = [GCF of 3,774,438]/[LCM of 31,23,21]= 3/14973
Therefore, the GCF of 3/31,774/23,438/21 is 3/14973.
To find the highest common factor of 3,774,438, we have to find the factors of both numbers and list the highest common factor.
The factors of 3 are 1, 3
The factors of 774 are 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, 774
The factors of 438 are 1, 2, 3, 6, 73, 146, 219, 438
The HCF of 3,774,438 is 3.
Lets's calculate GCF of 3,774,438
| 3 | 3, 774, 438 |
| 1, 258, 146 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 3,774,438 By Matching Biggest Common Factor Method
Now, list down the factors of 3
:1,3
Now, list down the factors of 774
:1,2,3,6,9,18,43,86,129,258,387,774
Now, list down the factors of 438
:1,2,3,6,73,146,219,438
Greatest Common Factor
We found the factors 3,774,438 . The biggest common factor number is the GCF number.
So the greatest common factor 3,774,438 is 3.
Lets's calculate LCM of 31,23,21
Given numbers has no common factors except 1. So, there LCM is their product i.e 14973
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/14973
Therefore, the GCF of Fractions 3/31,774/23,438/21 is 3/14973
Least Common Multiple of 31,23,21 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 31,23,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,23,21) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(31,23,21) x common factors =1 x 1 = 1
LCM(31,23,21) = ( 31 × 23 × 21 ) / 1
LCM(31,23,21) = 14973 / 1
LCM(31,23,21) = 14973
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FAQs on GCF of Fractions of 3/31, 774/23, 438/21
1. What is the HCF of 3,774,438?
The HCF of 3,774,438 is 3
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 3/31, 774/23, 438/21?
Answer: GCF of Numerators as per given numbers 3/31, 774/23, 438/21 is
GCF of Numerators i.e. for 3,774,438 is 3
LCM of denominators i.e. for 31,23,21 is 14973.
Thus, GCF of Fractions is 3/14973.Finally, GCF of Fractions for 3/31, 774/23, 438/21 is 3/14973.