GCF of 562/306, 4215/321
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 562/306, 4215/321 i.e 281/32742 easily. The following is the detailed procedure to determine the greatest common factor of fractions 562/306, 4215/321.
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 562/306,4215/321?
Given fractions are 562/306,4215/321
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 562/306,4215/321, numerators are 562,4215
Denominators are 306,321
The GCF of 562,4215 is 281 .
LCM of 306,321 is 32742.
The greatest common factor of 562/306,4215/321 = [GCF of 562,4215]/[LCM of 306,321]= 281/32742
Therefore, the GCF of 562/306,4215/321 is 281/32742.
To find the highest common factor of 562,4215, 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 4215 are 1, 3, 5, 15, 281, 843, 1405, 4215
The HCF of 562,4215 is 281.
Lets's calculate GCF of 562,4215
| 281 | 562, 4215 |
| 2, 15 |
∴ So the GCF of the given numbers is 281 = 281
Greatest Common Factor of 562,4215 By Matching Biggest Common Factor Method
Now, list down the factors of 562
:1,2,281,562
Now, list down the factors of 4215
:1,3,5,15,281,843,1405,4215
Greatest Common Factor
We found the factors 562,4215 . The biggest common factor number is the GCF number.
So the greatest common factor 562,4215 is 281.
Lets's calculate LCM of 306,321
| 3 | 306, 321 |
| 102, 107 |
∴ So the LCM of the given numbers is 3 x 102 x 107 = 32742
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 281/32742
Therefore, the GCF of Fractions 562/306,4215/321 is 281/32742
Least Common Multiple of 306,321 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 306,321 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(306,321) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(306,321) x common factors =3 x 1 = 3
LCM(306,321) = ( 306 × 321 ) / 3
LCM(306,321) = 98226 / 3
LCM(306,321) = 32742
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FAQs on GCF of Fractions of 562/306, 4215/321
1. What is the HCF of 562,4215?
The HCF of 562,4215 is 281
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 562/306, 4215/321?
Answer: GCF of Numerators as per given numbers 562/306, 4215/321 is
GCF of Numerators i.e. for 562,4215 is 281
LCM of denominators i.e. for 306,321 is 32742.
Thus, GCF of Fractions is 281/32742.Finally, GCF of Fractions for 562/306, 4215/321 is 281/32742.