GCF of 562/346, 5138/314
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 562/346, 5138/314 i.e 2/54322 easily. The following is the detailed procedure to determine the greatest common factor of fractions 562/346, 5138/314.
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 562/346,5138/314?
Given fractions are 562/346,5138/314
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 562/346,5138/314, numerators are 562,5138
Denominators are 346,314
The GCF of 562,5138 is 2 .
LCM of 346,314 is 54322.
The greatest common factor of 562/346,5138/314 = [GCF of 562,5138]/[LCM of 346,314]= 2/54322
Therefore, the GCF of 562/346,5138/314 is 2/54322.
To find the highest common factor of 562,5138, we have to find the factors of both numbers and list the highest common factor.
The factors of 562 are 1, 2, 281, 562
The factors of 5138 are 1, 2, 7, 14, 367, 734, 2569, 5138
The HCF of 562,5138 is 2.
Lets's calculate GCF of 562,5138
| 2 | 562, 5138 |
| 281, 2569 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 562,5138 By Matching Biggest Common Factor Method
Now, list down the factors of 562
:1,2,281,562
Now, list down the factors of 5138
:1,2,7,14,367,734,2569,5138
Greatest Common Factor
We found the factors 562,5138 . The biggest common factor number is the GCF number.
So the greatest common factor 562,5138 is 2.
Lets's calculate LCM of 346,314
| 2 | 346, 314 |
| 173, 157 |
∴ So the LCM of the given numbers is 2 x 173 x 157 = 54322
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/54322
Therefore, the GCF of Fractions 562/346,5138/314 is 2/54322
Least Common Multiple of 346,314 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 346,314 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(346,314) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(346,314) x common factors =2 x 1 = 2
LCM(346,314) = ( 346 × 314 ) / 2
LCM(346,314) = 108644 / 2
LCM(346,314) = 54322
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FAQs on GCF of Fractions of 562/346, 5138/314
1. What is the HCF of 562,5138?
The HCF of 562,5138 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 562/346, 5138/314?
Answer: GCF of Numerators as per given numbers 562/346, 5138/314 is
GCF of Numerators i.e. for 562,5138 is 2
LCM of denominators i.e. for 346,314 is 54322.
Thus, GCF of Fractions is 2/54322.Finally, GCF of Fractions for 562/346, 5138/314 is 2/54322.