GCF of 14/16, 587/54, 208/160
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 14/16, 587/54, 208/160 i.e 1/4320 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/16, 587/54, 208/160.
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 14/16,587/54,208/160?
Given fractions are 14/16,587/54,208/160
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 14/16,587/54,208/160, numerators are 14,587,208
Denominators are 16,54,160
The GCF of 14,587,208 is 1 .
LCM of 16,54,160 is 4320.
The greatest common factor of 14/16,587/54,208/160 = [GCF of 14,587,208]/[LCM of 16,54,160]= 1/4320
Therefore, the GCF of 14/16,587/54,208/160 is 1/4320.
To find the highest common factor of 14,587,208, we have to find the factors of both numbers and list the highest common factor.
The factors of 14 are 1, 2, 7, 14
The factors of 587 are 1, 587
The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208
The HCF of 14,587,208 is 1.
Lets's calculate GCF of 14,587,208
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 14,587,208 By Matching Biggest Common Factor Method
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 587
:1,587
Now, list down the factors of 208
:1,2,4,8,13,16,26,52,104,208
Greatest Common Factor
We found the factors 14,587,208 . The biggest common factor number is the GCF number.
So the greatest common factor 14,587,208 is 1.
Lets's calculate LCM of 16,54,160
| 2 | 16, 54, 160 |
| 2 | 8, 27, 80 |
| 2 | 4, 27, 40 |
| 2 | 2, 27, 20 |
| 1, 27, 10 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 1 x 27 x 10 = 4320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4320
Therefore, the GCF of Fractions 14/16,587/54,208/160 is 1/4320
Least Common Multiple of 16,54,160 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 16,54,160 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(16,54,160) = 2
common factors(in case of two or more numbers have common factors) = 16
GCF(16,54,160) x common factors =2 x 16 = 32
LCM(16,54,160) = ( 16 × 54 × 160 ) / 32
LCM(16,54,160) = 138240 / 32
LCM(16,54,160) = 4320
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FAQs on GCF of Fractions of 14/16, 587/54, 208/160
1. What is the HCF of 14,587,208?
The HCF of 14,587,208 is 1
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 14/16, 587/54, 208/160?
Answer: GCF of Numerators as per given numbers 14/16, 587/54, 208/160 is
GCF of Numerators i.e. for 14,587,208 is 1
LCM of denominators i.e. for 16,54,160 is 4320.
Thus, GCF of Fractions is 1/4320.Finally, GCF of Fractions for 14/16, 587/54, 208/160 is 1/4320.