GCF of 310/74, 378/5948
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 310/74, 378/5948 i.e 2/220076 easily. The following is the detailed procedure to determine the greatest common factor of fractions 310/74, 378/5948.
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 310/74,378/5948?
Given fractions are 310/74,378/5948
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 310/74,378/5948, numerators are 310,378
Denominators are 74,5948
The GCF of 310,378 is 2 .
LCM of 74,5948 is 220076.
The greatest common factor of 310/74,378/5948 = [GCF of 310,378]/[LCM of 74,5948]= 2/220076
Therefore, the GCF of 310/74,378/5948 is 2/220076.
To find the highest common factor of 310,378, we have to find the factors of both numbers and list the highest common factor.
The factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The HCF of 310,378 is 2.
Lets's calculate GCF of 310,378
| 2 | 310, 378 |
| 155, 189 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 310,378 By Matching Biggest Common Factor Method
Now, list down the factors of 310
:1,2,5,10,31,62,155,310
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 310,378 . The biggest common factor number is the GCF number.
So the greatest common factor 310,378 is 2.
Lets's calculate LCM of 74,5948
| 2 | 74, 5948 |
| 37, 2974 |
∴ So the LCM of the given numbers is 2 x 37 x 2974 = 220076
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/220076
Therefore, the GCF of Fractions 310/74,378/5948 is 2/220076
Least Common Multiple of 74,5948 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 74,5948 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,5948) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(74,5948) x common factors =2 x 1 = 2
LCM(74,5948) = ( 74 × 5948 ) / 2
LCM(74,5948) = 440152 / 2
LCM(74,5948) = 220076
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FAQs on GCF of Fractions of 310/74, 378/5948
1. What is the HCF of 310,378?
The HCF of 310,378 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 310/74, 378/5948?
Answer: GCF of Numerators as per given numbers 310/74, 378/5948 is
GCF of Numerators i.e. for 310,378 is 2
LCM of denominators i.e. for 74,5948 is 220076.
Thus, GCF of Fractions is 2/220076.Finally, GCF of Fractions for 310/74, 378/5948 is 2/220076.