Use our free GCF of Fractions Calculator tool to compute the GCF of 220/565, 492/409 i.e 4/231085 easily. The following is the detailed procedure to determine the greatest common factor of fractions 220/565, 492/409.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 220/565,492/409
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 220/565,492/409, numerators are 220,492
Denominators are 565,409
The GCF of 220,492 is 4 .
LCM of 565,409 is 231085.
The greatest common factor of 220/565,492/409 = [GCF of 220,492]/[LCM of 565,409]= 4/231085
Therefore, the GCF of 220/565,492/409 is 4/231085.
To find the highest common factor of 220,492, we have to find the factors of both numbers and list the highest common factor.
The factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220
The factors of 492 are 1, 2, 3, 4, 6, 12, 41, 82, 123, 164, 246, 492
The HCF of 220,492 is 4.
Lets's calculate GCF of 220,492
2 | 220, 492 |
2 | 110, 246 |
55, 123 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 220
:1,2,4,5,10,11,20,22,44,55,110,220
Now, list down the factors of 492
:1,2,3,4,6,12,41,82,123,164,246,492
Greatest Common Factor
We found the factors 220,492 . The biggest common factor number is the GCF number.
So the greatest common factor 220,492 is 4.
Lets's calculate LCM of 565,409
Given numbers has no common factors except 1. So, there LCM is their product i.e 231085
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/231085
Therefore, the GCF of Fractions 220/565,492/409 is 4/231085
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 565,409 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(565,409) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(565,409) x common factors =1 x 1 = 1
LCM(565,409) = ( 565 × 409 ) / 1
LCM(565,409) = 231085 / 1
LCM(565,409) = 231085
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 220,492?
The HCF of 220,492 is 4
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 220/565, 492/409?
Answer: GCF of Numerators as per given numbers 220/565, 492/409 is
GCF of Numerators i.e. for 220,492 is 4
LCM of denominators i.e. for 565,409 is 231085.
Thus, GCF of Fractions is 4/231085.Finally, GCF of Fractions for 220/565, 492/409 is 4/231085.