Use our free GCF of Fractions Calculator tool to compute the GCF of 222/743, 648/678 i.e 6/503754 easily. The following is the detailed procedure to determine the greatest common factor of fractions 222/743, 648/678.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 222/743,648/678
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 222/743,648/678, numerators are 222,648
Denominators are 743,678
The GCF of 222,648 is 6 .
LCM of 743,678 is 503754.
The greatest common factor of 222/743,648/678 = [GCF of 222,648]/[LCM of 743,678]= 6/503754
Therefore, the GCF of 222/743,648/678 is 6/503754.
To find the highest common factor of 222,648, we have to find the factors of both numbers and list the highest common factor.
The factors of 222 are 1, 2, 3, 6, 37, 74, 111, 222
The factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648
The HCF of 222,648 is 6.
Lets's calculate GCF of 222,648
2 | 222, 648 |
3 | 111, 324 |
37, 108 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 222
:1,2,3,6,37,74,111,222
Now, list down the factors of 648
:1,2,3,4,6,8,9,12,18,24,27,36,54,72,81,108,162,216,324,648
Greatest Common Factor
We found the factors 222,648 . The biggest common factor number is the GCF number.
So the greatest common factor 222,648 is 6.
Lets's calculate LCM of 743,678
Given numbers has no common factors except 1. So, there LCM is their product i.e 503754
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/503754
Therefore, the GCF of Fractions 222/743,648/678 is 6/503754
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 743,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(743,678) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(743,678) x common factors =1 x 1 = 1
LCM(743,678) = ( 743 × 678 ) / 1
LCM(743,678) = 503754 / 1
LCM(743,678) = 503754
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 222,648?
The HCF of 222,648 is 6
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 222/743, 648/678?
Answer: GCF of Numerators as per given numbers 222/743, 648/678 is
GCF of Numerators i.e. for 222,648 is 6
LCM of denominators i.e. for 743,678 is 503754.
Thus, GCF of Fractions is 6/503754.Finally, GCF of Fractions for 222/743, 648/678 is 6/503754.