Use our free GCF of Fractions Calculator tool to compute the GCF of 278/534, 522/762 i.e 2/67818 easily. The following is the detailed procedure to determine the greatest common factor of fractions 278/534, 522/762.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 278/534,522/762
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 278/534,522/762, numerators are 278,522
Denominators are 534,762
The GCF of 278,522 is 2 .
LCM of 534,762 is 67818.
The greatest common factor of 278/534,522/762 = [GCF of 278,522]/[LCM of 534,762]= 2/67818
Therefore, the GCF of 278/534,522/762 is 2/67818.
To find the highest common factor of 278,522, we have to find the factors of both numbers and list the highest common factor.
The factors of 278 are 1, 2, 139, 278
The factors of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522
The HCF of 278,522 is 2.
Lets's calculate GCF of 278,522
2 | 278, 522 |
139, 261 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 278
:1,2,139,278
Now, list down the factors of 522
:1,2,3,6,9,18,29,58,87,174,261,522
Greatest Common Factor
We found the factors 278,522 . The biggest common factor number is the GCF number.
So the greatest common factor 278,522 is 2.
Lets's calculate LCM of 534,762
2 | 534, 762 |
3 | 267, 381 |
89, 127 |
∴ So the LCM of the given numbers is 2 x 3 x 89 x 127 = 67818
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/67818
Therefore, the GCF of Fractions 278/534,522/762 is 2/67818
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 534,762 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(534,762) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(534,762) x common factors =6 x 1 = 6
LCM(534,762) = ( 534 × 762 ) / 6
LCM(534,762) = 406908 / 6
LCM(534,762) = 67818
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 278,522?
The HCF of 278,522 is 2
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 278/534, 522/762?
Answer: GCF of Numerators as per given numbers 278/534, 522/762 is
GCF of Numerators i.e. for 278,522 is 2
LCM of denominators i.e. for 534,762 is 67818.
Thus, GCF of Fractions is 2/67818.Finally, GCF of Fractions for 278/534, 522/762 is 2/67818.