Use our free GCF of Fractions Calculator tool to compute the GCF of 84/675, 630/744, 546/523 i.e 42/87550200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 84/675, 630/744, 546/523.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 84/675,630/744,546/523
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 84/675,630/744,546/523, numerators are 84,630,546
Denominators are 675,744,523
The GCF of 84,630,546 is 42 .
LCM of 675,744,523 is 87550200.
The greatest common factor of 84/675,630/744,546/523 = [GCF of 84,630,546]/[LCM of 675,744,523]= 42/87550200
Therefore, the GCF of 84/675,630/744,546/523 is 42/87550200.
To find the highest common factor of 84,630,546, 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 630 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630
The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
The HCF of 84,630,546 is 42.
Lets's calculate GCF of 84,630,546
2 | 84, 630, 546 |
3 | 42, 315, 273 |
7 | 14, 105, 91 |
2, 15, 13 |
∴ So the GCF of the given numbers is 2 x 3 x 7 = 42
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 630
:1,2,3,5,6,7,9,10,14,15,18,21,30,35,42,45,63,70,90,105,126,210,315,630
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 84,630,546 . The biggest common factor number is the GCF number.
So the greatest common factor 84,630,546 is 42.
Lets's calculate LCM of 675,744,523
3 | 675, 744, 523 |
225, 248, 523 |
∴ So the LCM of the given numbers is 3 x 225 x 248 x 523 = 87550200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 42/87550200
Therefore, the GCF of Fractions 84/675,630/744,546/523 is 42/87550200
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 675,744,523 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(675,744,523) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(675,744,523) x common factors =1 x 3 = 3
LCM(675,744,523) = ( 675 × 744 × 523 ) / 3
LCM(675,744,523) = 262650600 / 3
LCM(675,744,523) = 87550200
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 84,630,546?
The HCF of 84,630,546 is 42
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 84/675, 630/744, 546/523?
Answer: GCF of Numerators as per given numbers 84/675, 630/744, 546/523 is
GCF of Numerators i.e. for 84,630,546 is 42
LCM of denominators i.e. for 675,744,523 is 87550200.
Thus, GCF of Fractions is 42/87550200.Finally, GCF of Fractions for 84/675, 630/744, 546/523 is 42/87550200.