Use our free GCF of Fractions Calculator tool to compute the GCF of 700/158, 570/419 i.e 10/66202 easily. The following is the detailed procedure to determine the greatest common factor of fractions 700/158, 570/419.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 700/158,570/419
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 700/158,570/419, numerators are 700,570
Denominators are 158,419
The GCF of 700,570 is 10 .
LCM of 158,419 is 66202.
The greatest common factor of 700/158,570/419 = [GCF of 700,570]/[LCM of 158,419]= 10/66202
Therefore, the GCF of 700/158,570/419 is 10/66202.
To find the highest common factor of 700,570, we have to find the factors of both numbers and list the highest common factor.
The factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700
The factors of 570 are 1, 2, 3, 5, 6, 10, 15, 19, 30, 38, 57, 95, 114, 190, 285, 570
The HCF of 700,570 is 10.
Lets's calculate GCF of 700,570
2 | 700, 570 |
5 | 350, 285 |
70, 57 |
∴ So the GCF of the given numbers is 2 x 5 = 10
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
Now, list down the factors of 570
:1,2,3,5,6,10,15,19,30,38,57,95,114,190,285,570
Greatest Common Factor
We found the factors 700,570 . The biggest common factor number is the GCF number.
So the greatest common factor 700,570 is 10.
Lets's calculate LCM of 158,419
Given numbers has no common factors except 1. So, there LCM is their product i.e 66202
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/66202
Therefore, the GCF of Fractions 700/158,570/419 is 10/66202
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 158,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(158,419) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(158,419) x common factors =1 x 1 = 1
LCM(158,419) = ( 158 × 419 ) / 1
LCM(158,419) = 66202 / 1
LCM(158,419) = 66202
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 700,570?
The HCF of 700,570 is 10
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 700/158, 570/419?
Answer: GCF of Numerators as per given numbers 700/158, 570/419 is
GCF of Numerators i.e. for 700,570 is 10
LCM of denominators i.e. for 158,419 is 66202.
Thus, GCF of Fractions is 10/66202.Finally, GCF of Fractions for 700/158, 570/419 is 10/66202.