GCF of 828/10, 342/655
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 828/10, 342/655 i.e 18/1310 easily. The following is the detailed procedure to determine the greatest common factor of fractions 828/10, 342/655.
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 828/10,342/655?
Given fractions are 828/10,342/655
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 828/10,342/655, numerators are 828,342
Denominators are 10,655
The GCF of 828,342 is 18 .
LCM of 10,655 is 1310.
The greatest common factor of 828/10,342/655 = [GCF of 828,342]/[LCM of 10,655]= 18/1310
Therefore, the GCF of 828/10,342/655 is 18/1310.
To find the highest common factor of 828,342, we have to find the factors of both numbers and list the highest common factor.
The factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The HCF of 828,342 is 18.
Lets's calculate GCF of 828,342
| 2 | 828, 342 |
| 3 | 414, 171 |
| 3 | 138, 57 |
| 46, 19 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 828,342 By Matching Biggest Common Factor Method
Now, list down the factors of 828
:1,2,3,4,6,9,12,18,23,36,46,69,92,138,207,276,414,828
Now, list down the factors of 342
:1,2,3,6,9,18,19,38,57,114,171,342
Greatest Common Factor
We found the factors 828,342 . The biggest common factor number is the GCF number.
So the greatest common factor 828,342 is 18.
Lets's calculate LCM of 10,655
| 5 | 10, 655 |
| 2, 131 |
∴ So the LCM of the given numbers is 5 x 2 x 131 = 1310
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/1310
Therefore, the GCF of Fractions 828/10,342/655 is 18/1310
Least Common Multiple of 10,655 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 10,655 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(10,655) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(10,655) x common factors =5 x 1 = 5
LCM(10,655) = ( 10 × 655 ) / 5
LCM(10,655) = 6550 / 5
LCM(10,655) = 1310
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FAQs on GCF of Fractions of 828/10, 342/655
1. What is the HCF of 828,342?
The HCF of 828,342 is 18
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 828/10, 342/655?
Answer: GCF of Numerators as per given numbers 828/10, 342/655 is
GCF of Numerators i.e. for 828,342 is 18
LCM of denominators i.e. for 10,655 is 1310.
Thus, GCF of Fractions is 18/1310.Finally, GCF of Fractions for 828/10, 342/655 is 18/1310.