Use our free GCF of Fractions Calculator tool to compute the GCF of 84/105, 90/912, 546/772 i.e 6/6160560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 84/105, 90/912, 546/772.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 84/105,90/912,546/772
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 84/105,90/912,546/772, numerators are 84,90,546
Denominators are 105,912,772
The GCF of 84,90,546 is 6 .
LCM of 105,912,772 is 6160560.
The greatest common factor of 84/105,90/912,546/772 = [GCF of 84,90,546]/[LCM of 105,912,772]= 6/6160560
Therefore, the GCF of 84/105,90/912,546/772 is 6/6160560.
To find the highest common factor of 84,90,546, we have to find the factors of both numbers and list the highest common factor.
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
The HCF of 84,90,546 is 6.
Lets's calculate GCF of 84,90,546
2 | 84, 90, 546 |
3 | 42, 45, 273 |
14, 15, 91 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
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 546
:1,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546
Greatest Common Factor
We found the factors 84,90,546 . The biggest common factor number is the GCF number.
So the greatest common factor 84,90,546 is 6.
Lets's calculate LCM of 105,912,772
2 | 105, 912, 772 |
2 | 105, 456, 386 |
3 | 105, 228, 193 |
35, 76, 193 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 35 x 76 x 193 = 6160560
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/6160560
Therefore, the GCF of Fractions 84/105,90/912,546/772 is 6/6160560
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 105,912,772 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(105,912,772) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(105,912,772) x common factors =1 x 12 = 12
LCM(105,912,772) = ( 105 × 912 × 772 ) / 12
LCM(105,912,772) = 73926720 / 12
LCM(105,912,772) = 6160560
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 84,90,546?
The HCF of 84,90,546 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 84/105, 90/912, 546/772?
Answer: GCF of Numerators as per given numbers 84/105, 90/912, 546/772 is
GCF of Numerators i.e. for 84,90,546 is 6
LCM of denominators i.e. for 105,912,772 is 6160560.
Thus, GCF of Fractions is 6/6160560.Finally, GCF of Fractions for 84/105, 90/912, 546/772 is 6/6160560.