GCF of 864/66, 320/8160
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 864/66, 320/8160 i.e 32/89760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 864/66, 320/8160.
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 864/66,320/8160?
Given fractions are 864/66,320/8160
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 864/66,320/8160, numerators are 864,320
Denominators are 66,8160
The GCF of 864,320 is 32 .
LCM of 66,8160 is 89760.
The greatest common factor of 864/66,320/8160 = [GCF of 864,320]/[LCM of 66,8160]= 32/89760
Therefore, the GCF of 864/66,320/8160 is 32/89760.
To find the highest common factor of 864,320, we have to find the factors of both numbers and list the highest common factor.
The factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864
The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
The HCF of 864,320 is 32.
Lets's calculate GCF of 864,320
| 2 | 864, 320 |
| 2 | 432, 160 |
| 2 | 216, 80 |
| 2 | 108, 40 |
| 2 | 54, 20 |
| 27, 10 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32
Greatest Common Factor of 864,320 By Matching Biggest Common Factor Method
Now, list down the factors of 864
:1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,72,96,108,144,216,288,432,864
Now, list down the factors of 320
:1,2,4,5,8,10,16,20,32,40,64,80,160,320
Greatest Common Factor
We found the factors 864,320 . The biggest common factor number is the GCF number.
So the greatest common factor 864,320 is 32.
Lets's calculate LCM of 66,8160
| 2 | 66, 8160 |
| 3 | 33, 4080 |
| 11, 1360 |
∴ So the LCM of the given numbers is 2 x 3 x 11 x 1360 = 89760
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/89760
Therefore, the GCF of Fractions 864/66,320/8160 is 32/89760
Least Common Multiple of 66,8160 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 66,8160 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(66,8160) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(66,8160) x common factors =6 x 1 = 6
LCM(66,8160) = ( 66 × 8160 ) / 6
LCM(66,8160) = 538560 / 6
LCM(66,8160) = 89760
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FAQs on GCF of Fractions of 864/66, 320/8160
1. What is the HCF of 864,320?
The HCF of 864,320 is 32
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 864/66, 320/8160?
Answer: GCF of Numerators as per given numbers 864/66, 320/8160 is
GCF of Numerators i.e. for 864,320 is 32
LCM of denominators i.e. for 66,8160 is 89760.
Thus, GCF of Fractions is 32/89760.Finally, GCF of Fractions for 864/66, 320/8160 is 32/89760.