GCF of 34/440, 346/507, 378/674
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 34/440, 346/507, 378/674 i.e 2/75177960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/440, 346/507, 378/674.
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 34/440,346/507,378/674?
Given fractions are 34/440,346/507,378/674
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 34/440,346/507,378/674, numerators are 34,346,378
Denominators are 440,507,674
The GCF of 34,346,378 is 2 .
LCM of 440,507,674 is 75177960.
The greatest common factor of 34/440,346/507,378/674 = [GCF of 34,346,378]/[LCM of 440,507,674]= 2/75177960
Therefore, the GCF of 34/440,346/507,378/674 is 2/75177960.
To find the highest common factor of 34,346,378, we have to find the factors of both numbers and list the highest common factor.
The factors of 34 are 1, 2, 17, 34
The factors of 346 are 1, 2, 173, 346
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The HCF of 34,346,378 is 2.
Lets's calculate GCF of 34,346,378
| 2 | 34, 346, 378 |
| 17, 173, 189 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 34,346,378 By Matching Biggest Common Factor Method
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 346
:1,2,173,346
Now, list down the factors of 378
:1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Greatest Common Factor
We found the factors 34,346,378 . The biggest common factor number is the GCF number.
So the greatest common factor 34,346,378 is 2.
Lets's calculate LCM of 440,507,674
| 2 | 440, 507, 674 |
| 220, 507, 337 |
∴ So the LCM of the given numbers is 2 x 220 x 507 x 337 = 75177960
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/75177960
Therefore, the GCF of Fractions 34/440,346/507,378/674 is 2/75177960
Least Common Multiple of 440,507,674 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 440,507,674 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(440,507,674) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(440,507,674) x common factors =1 x 2 = 2
LCM(440,507,674) = ( 440 × 507 × 674 ) / 2
LCM(440,507,674) = 150355920 / 2
LCM(440,507,674) = 75177960
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 34/440, 346/507, 378/674
1. What is the HCF of 34,346,378?
The HCF of 34,346,378 is 2
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 34/440, 346/507, 378/674?
Answer: GCF of Numerators as per given numbers 34/440, 346/507, 378/674 is
GCF of Numerators i.e. for 34,346,378 is 2
LCM of denominators i.e. for 440,507,674 is 75177960.
Thus, GCF of Fractions is 2/75177960.Finally, GCF of Fractions for 34/440, 346/507, 378/674 is 2/75177960.