GCF of 13/51, 578/16, 284/154
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 13/51, 578/16, 284/154 i.e 1/62832 easily. The following is the detailed procedure to determine the greatest common factor of fractions 13/51, 578/16, 284/154.
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 13/51,578/16,284/154?
Given fractions are 13/51,578/16,284/154
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 13/51,578/16,284/154, numerators are 13,578,284
Denominators are 51,16,154
The GCF of 13,578,284 is 1 .
LCM of 51,16,154 is 62832.
The greatest common factor of 13/51,578/16,284/154 = [GCF of 13,578,284]/[LCM of 51,16,154]= 1/62832
Therefore, the GCF of 13/51,578/16,284/154 is 1/62832.
To find the highest common factor of 13,578,284, we have to find the factors of both numbers and list the highest common factor.
The factors of 13 are 1, 13
The factors of 578 are 1, 2, 17, 34, 289, 578
The factors of 284 are 1, 2, 4, 71, 142, 284
The HCF of 13,578,284 is 1.
Lets's calculate GCF of 13,578,284
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 13,578,284 By Matching Biggest Common Factor Method
Now, list down the factors of 13
:1,13
Now, list down the factors of 578
:1,2,17,34,289,578
Now, list down the factors of 284
:1,2,4,71,142,284
Greatest Common Factor
We found the factors 13,578,284 . The biggest common factor number is the GCF number.
So the greatest common factor 13,578,284 is 1.
Lets's calculate LCM of 51,16,154
| 2 | 51, 16, 154 |
| 51, 8, 77 |
∴ So the LCM of the given numbers is 2 x 51 x 8 x 77 = 62832
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/62832
Therefore, the GCF of Fractions 13/51,578/16,284/154 is 1/62832
Least Common Multiple of 51,16,154 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 51,16,154 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,16,154) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(51,16,154) x common factors =1 x 2 = 2
LCM(51,16,154) = ( 51 × 16 × 154 ) / 2
LCM(51,16,154) = 125664 / 2
LCM(51,16,154) = 62832
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FAQs on GCF of Fractions of 13/51, 578/16, 284/154
1. What is the HCF of 13,578,284?
The HCF of 13,578,284 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 13/51, 578/16, 284/154?
Answer: GCF of Numerators as per given numbers 13/51, 578/16, 284/154 is
GCF of Numerators i.e. for 13,578,284 is 1
LCM of denominators i.e. for 51,16,154 is 62832.
Thus, GCF of Fractions is 1/62832.Finally, GCF of Fractions for 13/51, 578/16, 284/154 is 1/62832.