GCF of 1760/368, 2256/585
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1760/368, 2256/585 i.e 16/215280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1760/368, 2256/585.
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 1760/368,2256/585?
Given fractions are 1760/368,2256/585
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 1760/368,2256/585, numerators are 1760,2256
Denominators are 368,585
The GCF of 1760,2256 is 16 .
LCM of 368,585 is 215280.
The greatest common factor of 1760/368,2256/585 = [GCF of 1760,2256]/[LCM of 368,585]= 16/215280
Therefore, the GCF of 1760/368,2256/585 is 16/215280.
To find the highest common factor of 1760,2256, we have to find the factors of both numbers and list the highest common factor.
The factors of 1760 are 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 32, 40, 44, 55, 80, 88, 110, 160, 176, 220, 352, 440, 880, 1760
The factors of 2256 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 47, 48, 94, 141, 188, 282, 376, 564, 752, 1128, 2256
The HCF of 1760,2256 is 16.
Lets's calculate GCF of 1760,2256
| 2 | 1760, 2256 |
| 2 | 880, 1128 |
| 2 | 440, 564 |
| 2 | 220, 282 |
| 110, 141 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Greatest Common Factor of 1760,2256 By Matching Biggest Common Factor Method
Now, list down the factors of 1760
:1,2,4,5,8,10,11,16,20,22,32,40,44,55,80,88,110,160,176,220,352,440,880,1760
Now, list down the factors of 2256
:1,2,3,4,6,8,12,16,24,47,48,94,141,188,282,376,564,752,1128,2256
Greatest Common Factor
We found the factors 1760,2256 . The biggest common factor number is the GCF number.
So the greatest common factor 1760,2256 is 16.
Lets's calculate LCM of 368,585
Given numbers has no common factors except 1. So, there LCM is their product i.e 215280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/215280
Therefore, the GCF of Fractions 1760/368,2256/585 is 16/215280
Least Common Multiple of 368,585 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 368,585 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(368,585) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(368,585) x common factors =1 x 1 = 1
LCM(368,585) = ( 368 × 585 ) / 1
LCM(368,585) = 215280 / 1
LCM(368,585) = 215280
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FAQs on GCF of Fractions of 1760/368, 2256/585
1. What is the HCF of 1760,2256?
The HCF of 1760,2256 is 16
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 1760/368, 2256/585?
Answer: GCF of Numerators as per given numbers 1760/368, 2256/585 is
GCF of Numerators i.e. for 1760,2256 is 16
LCM of denominators i.e. for 368,585 is 215280.
Thus, GCF of Fractions is 16/215280.Finally, GCF of Fractions for 1760/368, 2256/585 is 16/215280.