Use our free GCF of Fractions Calculator tool to compute the GCF of 220/17, 700/724 i.e 20/12308 easily. The following is the detailed procedure to determine the greatest common factor of fractions 220/17, 700/724.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 220/17,700/724
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 220/17,700/724, numerators are 220,700
Denominators are 17,724
The GCF of 220,700 is 20 .
LCM of 17,724 is 12308.
The greatest common factor of 220/17,700/724 = [GCF of 220,700]/[LCM of 17,724]= 20/12308
Therefore, the GCF of 220/17,700/724 is 20/12308.
To find the highest common factor of 220,700, 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 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700
The HCF of 220,700 is 20.
Lets's calculate GCF of 220,700
2 | 220, 700 |
2 | 110, 350 |
5 | 55, 175 |
11, 35 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
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 700
:1,2,4,5,7,10,14,20,25,28,35,50,70,100,140,175,350,700
Greatest Common Factor
We found the factors 220,700 . The biggest common factor number is the GCF number.
So the greatest common factor 220,700 is 20.
Lets's calculate LCM of 17,724
Given numbers has no common factors except 1. So, there LCM is their product i.e 12308
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/12308
Therefore, the GCF of Fractions 220/17,700/724 is 20/12308
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 17,724 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(17,724) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(17,724) x common factors =1 x 1 = 1
LCM(17,724) = ( 17 × 724 ) / 1
LCM(17,724) = 12308 / 1
LCM(17,724) = 12308
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 220,700?
The HCF of 220,700 is 20
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 220/17, 700/724?
Answer: GCF of Numerators as per given numbers 220/17, 700/724 is
GCF of Numerators i.e. for 220,700 is 20
LCM of denominators i.e. for 17,724 is 12308.
Thus, GCF of Fractions is 20/12308.Finally, GCF of Fractions for 220/17, 700/724 is 20/12308.