Use our free GCF of Fractions Calculator tool to compute the GCF of 570/523, 630/577 i.e 30/301771 easily. The following is the detailed procedure to determine the greatest common factor of fractions 570/523, 630/577.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 570/523,630/577
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 570/523,630/577, numerators are 570,630
Denominators are 523,577
The GCF of 570,630 is 30 .
LCM of 523,577 is 301771.
The greatest common factor of 570/523,630/577 = [GCF of 570,630]/[LCM of 523,577]= 30/301771
Therefore, the GCF of 570/523,630/577 is 30/301771.
To find the highest common factor of 570,630, we have to find the factors of both numbers and list the highest common factor.
The factors of 570 are 1, 2, 3, 5, 6, 10, 15, 19, 30, 38, 57, 95, 114, 190, 285, 570
The factors of 630 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630
The HCF of 570,630 is 30.
Lets's calculate GCF of 570,630
2 | 570, 630 |
3 | 285, 315 |
5 | 95, 105 |
19, 21 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Now, list down the factors of 570
:1,2,3,5,6,10,15,19,30,38,57,95,114,190,285,570
Now, list down the factors of 630
:1,2,3,5,6,7,9,10,14,15,18,21,30,35,42,45,63,70,90,105,126,210,315,630
Greatest Common Factor
We found the factors 570,630 . The biggest common factor number is the GCF number.
So the greatest common factor 570,630 is 30.
Lets's calculate LCM of 523,577
Given numbers has no common factors except 1. So, there LCM is their product i.e 301771
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/301771
Therefore, the GCF of Fractions 570/523,630/577 is 30/301771
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 523,577 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(523,577) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(523,577) x common factors =1 x 1 = 1
LCM(523,577) = ( 523 × 577 ) / 1
LCM(523,577) = 301771 / 1
LCM(523,577) = 301771
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 570,630?
The HCF of 570,630 is 30
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 570/523, 630/577?
Answer: GCF of Numerators as per given numbers 570/523, 630/577 is
GCF of Numerators i.e. for 570,630 is 30
LCM of denominators i.e. for 523,577 is 301771.
Thus, GCF of Fractions is 30/301771.Finally, GCF of Fractions for 570/523, 630/577 is 30/301771.