GCF of 704/660, 2112/640
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 704/660, 2112/640 i.e 704/21120 easily. The following is the detailed procedure to determine the greatest common factor of fractions 704/660, 2112/640.
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 704/660,2112/640?
Given fractions are 704/660,2112/640
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 704/660,2112/640, numerators are 704,2112
Denominators are 660,640
The GCF of 704,2112 is 704 .
LCM of 660,640 is 21120.
The greatest common factor of 704/660,2112/640 = [GCF of 704,2112]/[LCM of 660,640]= 704/21120
Therefore, the GCF of 704/660,2112/640 is 704/21120.
To find the highest common factor of 704,2112, we have to find the factors of both numbers and list the highest common factor.
The factors of 704 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352, 704
The factors of 2112 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 64, 66, 88, 96, 132, 176, 192, 264, 352, 528, 704, 1056, 2112
The HCF of 704,2112 is 704.
Lets's calculate GCF of 704,2112
| 2 | 704, 2112 |
| 2 | 352, 1056 |
| 2 | 176, 528 |
| 2 | 88, 264 |
| 2 | 44, 132 |
| 2 | 22, 66 |
| 11 | 11, 33 |
| 1, 3 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 x 11 = 704
Greatest Common Factor of 704,2112 By Matching Biggest Common Factor Method
Now, list down the factors of 704
:1,2,4,8,11,16,22,32,44,64,88,176,352,704
Now, list down the factors of 2112
:1,2,3,4,6,8,11,12,16,22,24,32,33,44,48,64,66,88,96,132,176,192,264,352,528,704,1056,2112
Greatest Common Factor
We found the factors 704,2112 . The biggest common factor number is the GCF number.
So the greatest common factor 704,2112 is 704.
Lets's calculate LCM of 660,640
| 2 | 660, 640 |
| 2 | 330, 320 |
| 5 | 165, 160 |
| 33, 32 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 33 x 32 = 21120
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 704/21120
Therefore, the GCF of Fractions 704/660,2112/640 is 704/21120
Least Common Multiple of 660,640 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 660,640 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(660,640) = 20
common factors(in case of two or more numbers have common factors) = 1
GCF(660,640) x common factors =20 x 1 = 20
LCM(660,640) = ( 660 × 640 ) / 20
LCM(660,640) = 422400 / 20
LCM(660,640) = 21120
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FAQs on GCF of Fractions of 704/660, 2112/640
1. What is the HCF of 704,2112?
The HCF of 704,2112 is 704
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 704/660, 2112/640?
Answer: GCF of Numerators as per given numbers 704/660, 2112/640 is
GCF of Numerators i.e. for 704,2112 is 704
LCM of denominators i.e. for 660,640 is 21120.
Thus, GCF of Fractions is 704/21120.Finally, GCF of Fractions for 704/660, 2112/640 is 704/21120.