GCF of 96/369, 54/693, 784/725
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 96/369, 54/693, 784/725 i.e 2/20599425 easily. The following is the detailed procedure to determine the greatest common factor of fractions 96/369, 54/693, 784/725.
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 96/369,54/693,784/725?
Given fractions are 96/369,54/693,784/725
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 96/369,54/693,784/725, numerators are 96,54,784
Denominators are 369,693,725
The GCF of 96,54,784 is 2 .
LCM of 369,693,725 is 20599425.
The greatest common factor of 96/369,54/693,784/725 = [GCF of 96,54,784]/[LCM of 369,693,725]= 2/20599425
Therefore, the GCF of 96/369,54/693,784/725 is 2/20599425.
To find the highest common factor of 96,54,784, we have to find the factors of both numbers and list the highest common factor.
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784
The HCF of 96,54,784 is 2.
Lets's calculate GCF of 96,54,784
| 2 | 96, 54, 784 |
| 48, 27, 392 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 96,54,784 By Matching Biggest Common Factor Method
Now, list down the factors of 96
:1,2,3,4,6,8,12,16,24,32,48,96
Now, list down the factors of 54
:1,2,3,6,9,18,27,54
Now, list down the factors of 784
:1,2,4,7,8,14,16,28,49,56,98,112,196,392,784
Greatest Common Factor
We found the factors 96,54,784 . The biggest common factor number is the GCF number.
So the greatest common factor 96,54,784 is 2.
Lets's calculate LCM of 369,693,725
| 3 | 369, 693, 725 |
| 3 | 123, 231, 725 |
| 41, 77, 725 |
∴ So the LCM of the given numbers is 3 x 3 x 41 x 77 x 725 = 20599425
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/20599425
Therefore, the GCF of Fractions 96/369,54/693,784/725 is 2/20599425
Least Common Multiple of 369,693,725 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 369,693,725 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(369,693,725) = 1
common factors(in case of two or more numbers have common factors) = 9
GCF(369,693,725) x common factors =1 x 9 = 9
LCM(369,693,725) = ( 369 × 693 × 725 ) / 9
LCM(369,693,725) = 185394825 / 9
LCM(369,693,725) = 20599425
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FAQs on GCF of Fractions of 96/369, 54/693, 784/725
1. What is the HCF of 96,54,784?
The HCF of 96,54,784 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 96/369, 54/693, 784/725?
Answer: GCF of Numerators as per given numbers 96/369, 54/693, 784/725 is
GCF of Numerators i.e. for 96,54,784 is 2
LCM of denominators i.e. for 369,693,725 is 20599425.
Thus, GCF of Fractions is 2/20599425.Finally, GCF of Fractions for 96/369, 54/693, 784/725 is 2/20599425.