Use our free GCF of Fractions Calculator tool to compute the GCF of 700/456, 500/165 i.e 100/25080 easily. The following is the detailed procedure to determine the greatest common factor of fractions 700/456, 500/165.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 700/456,500/165
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 700/456,500/165, numerators are 700,500
Denominators are 456,165
The GCF of 700,500 is 100 .
LCM of 456,165 is 25080.
The greatest common factor of 700/456,500/165 = [GCF of 700,500]/[LCM of 456,165]= 100/25080
Therefore, the GCF of 700/456,500/165 is 100/25080.
To find the highest common factor of 700,500, 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 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
The HCF of 700,500 is 100.
Lets's calculate GCF of 700,500
2 | 700, 500 |
2 | 350, 250 |
5 | 175, 125 |
5 | 35, 25 |
7, 5 |
∴ So the GCF of the given numbers is 2 x 2 x 5 x 5 = 100
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 500
:1,2,4,5,10,20,25,50,100,125,250,500
Greatest Common Factor
We found the factors 700,500 . The biggest common factor number is the GCF number.
So the greatest common factor 700,500 is 100.
Lets's calculate LCM of 456,165
3 | 456, 165 |
152, 55 |
∴ So the LCM of the given numbers is 3 x 152 x 55 = 25080
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 100/25080
Therefore, the GCF of Fractions 700/456,500/165 is 100/25080
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 456,165 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(456,165) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(456,165) x common factors =3 x 1 = 3
LCM(456,165) = ( 456 × 165 ) / 3
LCM(456,165) = 75240 / 3
LCM(456,165) = 25080
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 700,500?
The HCF of 700,500 is 100
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 700/456, 500/165?
Answer: GCF of Numerators as per given numbers 700/456, 500/165 is
GCF of Numerators i.e. for 700,500 is 100
LCM of denominators i.e. for 456,165 is 25080.
Thus, GCF of Fractions is 100/25080.Finally, GCF of Fractions for 700/456, 500/165 is 100/25080.