GCF of 64/21, 160/65, 352/110
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 64/21, 160/65, 352/110 i.e 32/30030 easily. The following is the detailed procedure to determine the greatest common factor of fractions 64/21, 160/65, 352/110.
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 64/21,160/65,352/110?
Given fractions are 64/21,160/65,352/110
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 64/21,160/65,352/110, numerators are 64,160,352
Denominators are 21,65,110
The GCF of 64,160,352 is 32 .
LCM of 21,65,110 is 30030.
The greatest common factor of 64/21,160/65,352/110 = [GCF of 64,160,352]/[LCM of 21,65,110]= 32/30030
Therefore, the GCF of 64/21,160/65,352/110 is 32/30030.
To find the highest common factor of 64,160,352, we have to find the factors of both numbers and list the highest common factor.
The factors of 64 are 1, 2, 4, 8, 16, 32, 64
The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160
The factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352
The HCF of 64,160,352 is 32.
Lets's calculate GCF of 64,160,352
| 2 | 64, 160, 352 |
| 2 | 32, 80, 176 |
| 2 | 16, 40, 88 |
| 2 | 8, 20, 44 |
| 2 | 4, 10, 22 |
| 2, 5, 11 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32
Greatest Common Factor of 64,160,352 By Matching Biggest Common Factor Method
Now, list down the factors of 64
:1,2,4,8,16,32,64
Now, list down the factors of 160
:1,2,4,5,8,10,16,20,32,40,80,160
Now, list down the factors of 352
:1,2,4,8,11,16,22,32,44,88,176,352
Greatest Common Factor
We found the factors 64,160,352 . The biggest common factor number is the GCF number.
So the greatest common factor 64,160,352 is 32.
Lets's calculate LCM of 21,65,110
| 5 | 21, 65, 110 |
| 21, 13, 22 |
∴ So the LCM of the given numbers is 5 x 21 x 13 x 22 = 30030
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/30030
Therefore, the GCF of Fractions 64/21,160/65,352/110 is 32/30030
Least Common Multiple of 21,65,110 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 21,65,110 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,65,110) = 1
common factors(in case of two or more numbers have common factors) = 5
GCF(21,65,110) x common factors =1 x 5 = 5
LCM(21,65,110) = ( 21 × 65 × 110 ) / 5
LCM(21,65,110) = 150150 / 5
LCM(21,65,110) = 30030
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FAQs on GCF of Fractions of 64/21, 160/65, 352/110
1. What is the HCF of 64,160,352?
The HCF of 64,160,352 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 64/21, 160/65, 352/110?
Answer: GCF of Numerators as per given numbers 64/21, 160/65, 352/110 is
GCF of Numerators i.e. for 64,160,352 is 32
LCM of denominators i.e. for 21,65,110 is 30030.
Thus, GCF of Fractions is 32/30030.Finally, GCF of Fractions for 64/21, 160/65, 352/110 is 32/30030.