Use our free GCF of Fractions Calculator tool to compute the GCF of 630/606, 420/699 i.e 210/141198 easily. The following is the detailed procedure to determine the greatest common factor of fractions 630/606, 420/699.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 630/606,420/699
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 630/606,420/699, numerators are 630,420
Denominators are 606,699
The GCF of 630,420 is 210 .
LCM of 606,699 is 141198.
The greatest common factor of 630/606,420/699 = [GCF of 630,420]/[LCM of 606,699]= 210/141198
Therefore, the GCF of 630/606,420/699 is 210/141198.
To find the highest common factor of 630,420, we have to find the factors of both numbers and list the highest common factor.
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 factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 630,420 is 210.
Lets's calculate GCF of 630,420
2 | 630, 420 |
3 | 315, 210 |
5 | 105, 70 |
7 | 21, 14 |
3, 2 |
∴ So the GCF of the given numbers is 2 x 3 x 5 x 7 = 210
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
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 630,420 . The biggest common factor number is the GCF number.
So the greatest common factor 630,420 is 210.
Lets's calculate LCM of 606,699
3 | 606, 699 |
202, 233 |
∴ So the LCM of the given numbers is 3 x 202 x 233 = 141198
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 210/141198
Therefore, the GCF of Fractions 630/606,420/699 is 210/141198
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 606,699 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(606,699) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(606,699) x common factors =3 x 1 = 3
LCM(606,699) = ( 606 × 699 ) / 3
LCM(606,699) = 423594 / 3
LCM(606,699) = 141198
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 630,420?
The HCF of 630,420 is 210
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 630/606, 420/699?
Answer: GCF of Numerators as per given numbers 630/606, 420/699 is
GCF of Numerators i.e. for 630,420 is 210
LCM of denominators i.e. for 606,699 is 141198.
Thus, GCF of Fractions is 210/141198.Finally, GCF of Fractions for 630/606, 420/699 is 210/141198.