GCF of 285/30, 714/542
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 285/30, 714/542 i.e 3/8130 easily. The following is the detailed procedure to determine the greatest common factor of fractions 285/30, 714/542.
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 285/30,714/542?
Given fractions are 285/30,714/542
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 285/30,714/542, numerators are 285,714
Denominators are 30,542
The GCF of 285,714 is 3 .
LCM of 30,542 is 8130.
The greatest common factor of 285/30,714/542 = [GCF of 285,714]/[LCM of 30,542]= 3/8130
Therefore, the GCF of 285/30,714/542 is 3/8130.
To find the highest common factor of 285,714, we have to find the factors of both numbers and list the highest common factor.
The factors of 285 are 1, 3, 5, 15, 19, 57, 95, 285
The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714
The HCF of 285,714 is 3.
Lets's calculate GCF of 285,714
| 3 | 285, 714 |
| 95, 238 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 285,714 By Matching Biggest Common Factor Method
Now, list down the factors of 285
:1,3,5,15,19,57,95,285
Now, list down the factors of 714
:1,2,3,6,7,14,17,21,34,42,51,102,119,238,357,714
Greatest Common Factor
We found the factors 285,714 . The biggest common factor number is the GCF number.
So the greatest common factor 285,714 is 3.
Lets's calculate LCM of 30,542
| 2 | 30, 542 |
| 15, 271 |
∴ So the LCM of the given numbers is 2 x 15 x 271 = 8130
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/8130
Therefore, the GCF of Fractions 285/30,714/542 is 3/8130
Least Common Multiple of 30,542 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 30,542 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,542) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(30,542) x common factors =2 x 1 = 2
LCM(30,542) = ( 30 × 542 ) / 2
LCM(30,542) = 16260 / 2
LCM(30,542) = 8130
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FAQs on GCF of Fractions of 285/30, 714/542
1. What is the HCF of 285,714?
The HCF of 285,714 is 3
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 285/30, 714/542?
Answer: GCF of Numerators as per given numbers 285/30, 714/542 is
GCF of Numerators i.e. for 285,714 is 3
LCM of denominators i.e. for 30,542 is 8130.
Thus, GCF of Fractions is 3/8130.Finally, GCF of Fractions for 285/30, 714/542 is 3/8130.