GCF of 2280/778, 1824/1052
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2280/778, 1824/1052 i.e 456/409228 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2280/778, 1824/1052.
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 2280/778,1824/1052?
Given fractions are 2280/778,1824/1052
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 2280/778,1824/1052, numerators are 2280,1824
Denominators are 778,1052
The GCF of 2280,1824 is 456 .
LCM of 778,1052 is 409228.
The greatest common factor of 2280/778,1824/1052 = [GCF of 2280,1824]/[LCM of 778,1052]= 456/409228
Therefore, the GCF of 2280/778,1824/1052 is 456/409228.
To find the highest common factor of 2280,1824, we have to find the factors of both numbers and list the highest common factor.
The factors of 2280 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 19, 20, 24, 30, 38, 40, 57, 60, 76, 95, 114, 120, 152, 190, 228, 285, 380, 456, 570, 760, 1140, 2280
The factors of 1824 are 1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 76, 96, 114, 152, 228, 304, 456, 608, 912, 1824
The HCF of 2280,1824 is 456.
Lets's calculate GCF of 2280,1824
| 2 | 2280, 1824 |
| 2 | 1140, 912 |
| 2 | 570, 456 |
| 3 | 285, 228 |
| 19 | 95, 76 |
| 5, 4 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 x 19 = 456
Greatest Common Factor of 2280,1824 By Matching Biggest Common Factor Method
Now, list down the factors of 2280
:1,2,3,4,5,6,8,10,12,15,19,20,24,30,38,40,57,60,76,95,114,120,152,190,228,285,380,456,570,760,1140,2280
Now, list down the factors of 1824
:1,2,3,4,6,8,12,16,19,24,32,38,48,57,76,96,114,152,228,304,456,608,912,1824
Greatest Common Factor
We found the factors 2280,1824 . The biggest common factor number is the GCF number.
So the greatest common factor 2280,1824 is 456.
Lets's calculate LCM of 778,1052
| 2 | 778, 1052 |
| 389, 526 |
∴ So the LCM of the given numbers is 2 x 389 x 526 = 409228
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 456/409228
Therefore, the GCF of Fractions 2280/778,1824/1052 is 456/409228
Least Common Multiple of 778,1052 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 778,1052 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(778,1052) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(778,1052) x common factors =2 x 1 = 2
LCM(778,1052) = ( 778 × 1052 ) / 2
LCM(778,1052) = 818456 / 2
LCM(778,1052) = 409228
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 2280/778, 1824/1052
1. What is the HCF of 2280,1824?
The HCF of 2280,1824 is 456
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 2280/778, 1824/1052?
Answer: GCF of Numerators as per given numbers 2280/778, 1824/1052 is
GCF of Numerators i.e. for 2280,1824 is 456
LCM of denominators i.e. for 778,1052 is 409228.
Thus, GCF of Fractions is 456/409228.Finally, GCF of Fractions for 2280/778, 1824/1052 is 456/409228.