Use our free GCF of Fractions Calculator tool to compute the GCF of 90/44, 312/75, 352/225 i.e 2/9900 easily. The following is the detailed procedure to determine the greatest common factor of fractions 90/44, 312/75, 352/225.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 90/44,312/75,352/225
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 90/44,312/75,352/225, numerators are 90,312,352
Denominators are 44,75,225
The GCF of 90,312,352 is 2 .
LCM of 44,75,225 is 9900.
The greatest common factor of 90/44,312/75,352/225 = [GCF of 90,312,352]/[LCM of 44,75,225]= 2/9900
Therefore, the GCF of 90/44,312/75,352/225 is 2/9900.
To find the highest common factor of 90,312,352, we have to find the factors of both numbers and list the highest common factor.
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352
The HCF of 90,312,352 is 2.
Lets's calculate GCF of 90,312,352
2 | 90, 312, 352 |
45, 156, 176 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 90
:1,2,3,5,6,9,10,15,18,30,45,90
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Now, list down the factors of 352
:1,2,4,8,11,16,22,32,44,88,176,352
Greatest Common Factor
We found the factors 90,312,352 . The biggest common factor number is the GCF number.
So the greatest common factor 90,312,352 is 2.
Lets's calculate LCM of 44,75,225
3 | 44, 75, 225 |
5 | 44, 25, 75 |
5 | 44, 5, 15 |
44, 1, 3 |
∴ So the LCM of the given numbers is 3 x 5 x 5 x 44 x 1 x 3 = 9900
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/9900
Therefore, the GCF of Fractions 90/44,312/75,352/225 is 2/9900
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 44,75,225 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(44,75,225) = 1
common factors(in case of two or more numbers have common factors) = 75
GCF(44,75,225) x common factors =1 x 75 = 75
LCM(44,75,225) = ( 44 × 75 × 225 ) / 75
LCM(44,75,225) = 742500 / 75
LCM(44,75,225) = 9900
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 90,312,352?
The HCF of 90,312,352 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 90/44, 312/75, 352/225?
Answer: GCF of Numerators as per given numbers 90/44, 312/75, 352/225 is
GCF of Numerators i.e. for 90,312,352 is 2
LCM of denominators i.e. for 44,75,225 is 9900.
Thus, GCF of Fractions is 2/9900.Finally, GCF of Fractions for 90/44, 312/75, 352/225 is 2/9900.