GCF of 12/133, 72/784, 456/448
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 12/133, 72/784, 456/448 i.e 12/59584 easily. The following is the detailed procedure to determine the greatest common factor of fractions 12/133, 72/784, 456/448.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 12/133,72/784,456/448?
Given fractions are 12/133,72/784,456/448
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 12/133,72/784,456/448, numerators are 12,72,456
Denominators are 133,784,448
The GCF of 12,72,456 is 12 .
LCM of 133,784,448 is 59584.
The greatest common factor of 12/133,72/784,456/448 = [GCF of 12,72,456]/[LCM of 133,784,448]= 12/59584
Therefore, the GCF of 12/133,72/784,456/448 is 12/59584.
To find the highest common factor of 12,72,456, we have to find the factors of both numbers and list the highest common factor.
The factors of 12 are 1, 2, 3, 4, 6, 12
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
The HCF of 12,72,456 is 12.
Lets's calculate GCF of 12,72,456
| 2 | 12, 72, 456 |
| 2 | 6, 36, 228 |
| 3 | 3, 18, 114 |
| 1, 6, 38 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 12,72,456 By Matching Biggest Common Factor Method
Now, list down the factors of 12
:1,2,3,4,6,12
Now, list down the factors of 72
:1,2,3,4,6,8,9,12,18,24,36,72
Now, list down the factors of 456
:1,2,3,4,6,8,12,19,24,38,57,76,114,152,228,456
Greatest Common Factor
We found the factors 12,72,456 . The biggest common factor number is the GCF number.
So the greatest common factor 12,72,456 is 12.
Lets's calculate LCM of 133,784,448
| 2 | 133, 784, 448 |
| 2 | 133, 392, 224 |
| 2 | 133, 196, 112 |
| 2 | 133, 98, 56 |
| 7 | 133, 49, 28 |
| 19, 7, 4 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 7 x 19 x 7 x 4 = 59584
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/59584
Therefore, the GCF of Fractions 12/133,72/784,456/448 is 12/59584
Least Common Multiple of 133,784,448 with GCF Formula
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 133,784,448 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(133,784,448) = 7
common factors(in case of two or more numbers have common factors) = 112
GCF(133,784,448) x common factors =7 x 112 = 784
LCM(133,784,448) = ( 133 × 784 × 448 ) / 784
LCM(133,784,448) = 46713856 / 784
LCM(133,784,448) = 59584
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 12/133, 72/784, 456/448
1. What is the HCF of 12,72,456?
The HCF of 12,72,456 is 12
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 12/133, 72/784, 456/448?
Answer: GCF of Numerators as per given numbers 12/133, 72/784, 456/448 is
GCF of Numerators i.e. for 12,72,456 is 12
LCM of denominators i.e. for 133,784,448 is 59584.
Thus, GCF of Fractions is 12/59584.Finally, GCF of Fractions for 12/133, 72/784, 456/448 is 12/59584.