Use our free GCF of Fractions Calculator tool to compute the GCF of 14/120, 45/856, 527/648 i.e 1/346680 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/120, 45/856, 527/648.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 14/120,45/856,527/648
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 14/120,45/856,527/648, numerators are 14,45,527
Denominators are 120,856,648
The GCF of 14,45,527 is 1 .
LCM of 120,856,648 is 346680.
The greatest common factor of 14/120,45/856,527/648 = [GCF of 14,45,527]/[LCM of 120,856,648]= 1/346680
Therefore, the GCF of 14/120,45/856,527/648 is 1/346680.
To find the highest common factor of 14,45,527, we have to find the factors of both numbers and list the highest common factor.
The factors of 14 are 1, 2, 7, 14
The factors of 45 are 1, 3, 5, 9, 15, 45
The factors of 527 are 1, 17, 31, 527
The HCF of 14,45,527 is 1.
Lets's calculate GCF of 14,45,527
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 45
:1,3,5,9,15,45
Now, list down the factors of 527
:1,17,31,527
Greatest Common Factor
We found the factors 14,45,527 . The biggest common factor number is the GCF number.
So the greatest common factor 14,45,527 is 1.
Lets's calculate LCM of 120,856,648
2 | 120, 856, 648 |
2 | 60, 428, 324 |
2 | 30, 214, 162 |
3 | 15, 107, 81 |
5, 107, 27 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 5 x 107 x 27 = 346680
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/346680
Therefore, the GCF of Fractions 14/120,45/856,527/648 is 1/346680
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 120,856,648 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(120,856,648) = 8
common factors(in case of two or more numbers have common factors) = 24
GCF(120,856,648) x common factors =8 x 24 = 192
LCM(120,856,648) = ( 120 × 856 × 648 ) / 192
LCM(120,856,648) = 66562560 / 192
LCM(120,856,648) = 346680
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 14,45,527?
The HCF of 14,45,527 is 1
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 14/120, 45/856, 527/648?
Answer: GCF of Numerators as per given numbers 14/120, 45/856, 527/648 is
GCF of Numerators i.e. for 14,45,527 is 1
LCM of denominators i.e. for 120,856,648 is 346680.
Thus, GCF of Fractions is 1/346680.Finally, GCF of Fractions for 14/120, 45/856, 527/648 is 1/346680.