Use our free GCF of Fractions Calculator tool to compute the GCF of 756/216, 420/148 i.e 84/7992 easily. The following is the detailed procedure to determine the greatest common factor of fractions 756/216, 420/148.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 756/216,420/148
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 756/216,420/148, numerators are 756,420
Denominators are 216,148
The GCF of 756,420 is 84 .
LCM of 216,148 is 7992.
The greatest common factor of 756/216,420/148 = [GCF of 756,420]/[LCM of 216,148]= 84/7992
Therefore, the GCF of 756/216,420/148 is 84/7992.
To find the highest common factor of 756,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 756 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756
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 756,420 is 84.
Lets's calculate GCF of 756,420
2 | 756, 420 |
2 | 378, 210 |
3 | 189, 105 |
7 | 63, 35 |
9, 5 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 7 = 84
Now, list down the factors of 756
:1,2,3,4,6,7,9,12,14,18,21,27,28,36,42,54,63,84,108,126,189,252,378,756
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 756,420 . The biggest common factor number is the GCF number.
So the greatest common factor 756,420 is 84.
Lets's calculate LCM of 216,148
2 | 216, 148 |
2 | 108, 74 |
54, 37 |
∴ So the LCM of the given numbers is 2 x 2 x 54 x 37 = 7992
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 84/7992
Therefore, the GCF of Fractions 756/216,420/148 is 84/7992
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 216,148 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(216,148) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(216,148) x common factors =4 x 1 = 4
LCM(216,148) = ( 216 × 148 ) / 4
LCM(216,148) = 31968 / 4
LCM(216,148) = 7992
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 756,420?
The HCF of 756,420 is 84
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 756/216, 420/148?
Answer: GCF of Numerators as per given numbers 756/216, 420/148 is
GCF of Numerators i.e. for 756,420 is 84
LCM of denominators i.e. for 216,148 is 7992.
Thus, GCF of Fractions is 84/7992.Finally, GCF of Fractions for 756/216, 420/148 is 84/7992.