GCF of 542/609, 314/362
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 542/609, 314/362 i.e 2/220458 easily. The following is the detailed procedure to determine the greatest common factor of fractions 542/609, 314/362.
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 542/609,314/362?
Given fractions are 542/609,314/362
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 542/609,314/362, numerators are 542,314
Denominators are 609,362
The GCF of 542,314 is 2 .
LCM of 609,362 is 220458.
The greatest common factor of 542/609,314/362 = [GCF of 542,314]/[LCM of 609,362]= 2/220458
Therefore, the GCF of 542/609,314/362 is 2/220458.
To find the highest common factor of 542,314, we have to find the factors of both numbers and list the highest common factor.
The factors of 542 are 1, 2, 271, 542
The factors of 314 are 1, 2, 157, 314
The HCF of 542,314 is 2.
Lets's calculate GCF of 542,314
| 2 | 542, 314 |
| 271, 157 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 542,314 By Matching Biggest Common Factor Method
Now, list down the factors of 542
:1,2,271,542
Now, list down the factors of 314
:1,2,157,314
Greatest Common Factor
We found the factors 542,314 . The biggest common factor number is the GCF number.
So the greatest common factor 542,314 is 2.
Lets's calculate LCM of 609,362
Given numbers has no common factors except 1. So, there LCM is their product i.e 220458
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/220458
Therefore, the GCF of Fractions 542/609,314/362 is 2/220458
Least Common Multiple of 609,362 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 609,362 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(609,362) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(609,362) x common factors =1 x 1 = 1
LCM(609,362) = ( 609 × 362 ) / 1
LCM(609,362) = 220458 / 1
LCM(609,362) = 220458
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FAQs on GCF of Fractions of 542/609, 314/362
1. What is the HCF of 542,314?
The HCF of 542,314 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 542/609, 314/362?
Answer: GCF of Numerators as per given numbers 542/609, 314/362 is
GCF of Numerators i.e. for 542,314 is 2
LCM of denominators i.e. for 609,362 is 220458.
Thus, GCF of Fractions is 2/220458.Finally, GCF of Fractions for 542/609, 314/362 is 2/220458.