GCF of 783/268, 312/512
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 783/268, 312/512 i.e 3/34304 easily. The following is the detailed procedure to determine the greatest common factor of fractions 783/268, 312/512.
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 783/268,312/512?
Given fractions are 783/268,312/512
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 783/268,312/512, numerators are 783,312
Denominators are 268,512
The GCF of 783,312 is 3 .
LCM of 268,512 is 34304.
The greatest common factor of 783/268,312/512 = [GCF of 783,312]/[LCM of 268,512]= 3/34304
Therefore, the GCF of 783/268,312/512 is 3/34304.
To find the highest common factor of 783,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 783 are 1, 3, 9, 27, 29, 87, 261, 783
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 783,312 is 3.
Lets's calculate GCF of 783,312
| 3 | 783, 312 |
| 261, 104 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 783,312 By Matching Biggest Common Factor Method
Now, list down the factors of 783
:1,3,9,27,29,87,261,783
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 783,312 . The biggest common factor number is the GCF number.
So the greatest common factor 783,312 is 3.
Lets's calculate LCM of 268,512
| 2 | 268, 512 |
| 2 | 134, 256 |
| 67, 128 |
∴ So the LCM of the given numbers is 2 x 2 x 67 x 128 = 34304
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/34304
Therefore, the GCF of Fractions 783/268,312/512 is 3/34304
Least Common Multiple of 268,512 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 268,512 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(268,512) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(268,512) x common factors =4 x 1 = 4
LCM(268,512) = ( 268 × 512 ) / 4
LCM(268,512) = 137216 / 4
LCM(268,512) = 34304
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FAQs on GCF of Fractions of 783/268, 312/512
1. What is the HCF of 783,312?
The HCF of 783,312 is 3
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 783/268, 312/512?
Answer: GCF of Numerators as per given numbers 783/268, 312/512 is
GCF of Numerators i.e. for 783,312 is 3
LCM of denominators i.e. for 268,512 is 34304.
Thus, GCF of Fractions is 3/34304.Finally, GCF of Fractions for 783/268, 312/512 is 3/34304.