GCF of 268/278, 784/132
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 268/278, 784/132 i.e 4/18348 easily. The following is the detailed procedure to determine the greatest common factor of fractions 268/278, 784/132.
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 268/278,784/132?
Given fractions are 268/278,784/132
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 268/278,784/132, numerators are 268,784
Denominators are 278,132
The GCF of 268,784 is 4 .
LCM of 278,132 is 18348.
The greatest common factor of 268/278,784/132 = [GCF of 268,784]/[LCM of 278,132]= 4/18348
Therefore, the GCF of 268/278,784/132 is 4/18348.
To find the highest common factor of 268,784, we have to find the factors of both numbers and list the highest common factor.
The factors of 268 are 1, 2, 4, 67, 134, 268
The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784
The HCF of 268,784 is 4.
Lets's calculate GCF of 268,784
| 2 | 268, 784 |
| 2 | 134, 392 |
| 67, 196 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 268,784 By Matching Biggest Common Factor Method
Now, list down the factors of 268
:1,2,4,67,134,268
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 268,784 . The biggest common factor number is the GCF number.
So the greatest common factor 268,784 is 4.
Lets's calculate LCM of 278,132
| 2 | 278, 132 |
| 139, 66 |
∴ So the LCM of the given numbers is 2 x 139 x 66 = 18348
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/18348
Therefore, the GCF of Fractions 268/278,784/132 is 4/18348
Least Common Multiple of 278,132 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 278,132 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(278,132) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(278,132) x common factors =2 x 1 = 2
LCM(278,132) = ( 278 × 132 ) / 2
LCM(278,132) = 36696 / 2
LCM(278,132) = 18348
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FAQs on GCF of Fractions of 268/278, 784/132
1. What is the HCF of 268,784?
The HCF of 268,784 is 4
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 268/278, 784/132?
Answer: GCF of Numerators as per given numbers 268/278, 784/132 is
GCF of Numerators i.e. for 268,784 is 4
LCM of denominators i.e. for 278,132 is 18348.
Thus, GCF of Fractions is 4/18348.Finally, GCF of Fractions for 268/278, 784/132 is 4/18348.