Use our free GCF of Fractions Calculator tool to compute the GCF of 700/182, 825/269 i.e 25/48958 easily. The following is the detailed procedure to determine the greatest common factor of fractions 700/182, 825/269.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 700/182,825/269
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 700/182,825/269, numerators are 700,825
Denominators are 182,269
The GCF of 700,825 is 25 .
LCM of 182,269 is 48958.
The greatest common factor of 700/182,825/269 = [GCF of 700,825]/[LCM of 182,269]= 25/48958
Therefore, the GCF of 700/182,825/269 is 25/48958.
To find the highest common factor of 700,825, 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 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825
The HCF of 700,825 is 25.
Lets's calculate GCF of 700,825
5 | 700, 825 |
5 | 140, 165 |
28, 33 |
∴ So the GCF of the given numbers is 5 x 5 = 25
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 825
:1,3,5,11,15,25,33,55,75,165,275,825
Greatest Common Factor
We found the factors 700,825 . The biggest common factor number is the GCF number.
So the greatest common factor 700,825 is 25.
Lets's calculate LCM of 182,269
Given numbers has no common factors except 1. So, there LCM is their product i.e 48958
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 25/48958
Therefore, the GCF of Fractions 700/182,825/269 is 25/48958
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 182,269 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(182,269) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(182,269) x common factors =1 x 1 = 1
LCM(182,269) = ( 182 × 269 ) / 1
LCM(182,269) = 48958 / 1
LCM(182,269) = 48958
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 700,825?
The HCF of 700,825 is 25
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 700/182, 825/269?
Answer: GCF of Numerators as per given numbers 700/182, 825/269 is
GCF of Numerators i.e. for 700,825 is 25
LCM of denominators i.e. for 182,269 is 48958.
Thus, GCF of Fractions is 25/48958.Finally, GCF of Fractions for 700/182, 825/269 is 25/48958.