GCF of 3075/102, 3738/4758
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3075/102, 3738/4758 i.e 3/80886 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3075/102, 3738/4758.
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 3075/102,3738/4758?
Given fractions are 3075/102,3738/4758
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 3075/102,3738/4758, numerators are 3075,3738
Denominators are 102,4758
The GCF of 3075,3738 is 3 .
LCM of 102,4758 is 80886.
The greatest common factor of 3075/102,3738/4758 = [GCF of 3075,3738]/[LCM of 102,4758]= 3/80886
Therefore, the GCF of 3075/102,3738/4758 is 3/80886.
To find the highest common factor of 3075,3738, we have to find the factors of both numbers and list the highest common factor.
The factors of 3075 are 1, 3, 5, 15, 25, 41, 75, 123, 205, 615, 1025, 3075
The factors of 3738 are 1, 2, 3, 6, 7, 14, 21, 42, 89, 178, 267, 534, 623, 1246, 1869, 3738
The HCF of 3075,3738 is 3.
Lets's calculate GCF of 3075,3738
| 3 | 3075, 3738 |
| 1025, 1246 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 3075,3738 By Matching Biggest Common Factor Method
Now, list down the factors of 3075
:1,3,5,15,25,41,75,123,205,615,1025,3075
Now, list down the factors of 3738
:1,2,3,6,7,14,21,42,89,178,267,534,623,1246,1869,3738
Greatest Common Factor
We found the factors 3075,3738 . The biggest common factor number is the GCF number.
So the greatest common factor 3075,3738 is 3.
Lets's calculate LCM of 102,4758
| 2 | 102, 4758 |
| 3 | 51, 2379 |
| 17, 793 |
∴ So the LCM of the given numbers is 2 x 3 x 17 x 793 = 80886
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/80886
Therefore, the GCF of Fractions 3075/102,3738/4758 is 3/80886
Least Common Multiple of 102,4758 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 102,4758 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(102,4758) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(102,4758) x common factors =6 x 1 = 6
LCM(102,4758) = ( 102 × 4758 ) / 6
LCM(102,4758) = 485316 / 6
LCM(102,4758) = 80886
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FAQs on GCF of Fractions of 3075/102, 3738/4758
1. What is the HCF of 3075,3738?
The HCF of 3075,3738 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 3075/102, 3738/4758?
Answer: GCF of Numerators as per given numbers 3075/102, 3738/4758 is
GCF of Numerators i.e. for 3075,3738 is 3
LCM of denominators i.e. for 102,4758 is 80886.
Thus, GCF of Fractions is 3/80886.Finally, GCF of Fractions for 3075/102, 3738/4758 is 3/80886.