GCF of 564/54, 870/141
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 564/54, 870/141 i.e 6/2538 easily. The following is the detailed procedure to determine the greatest common factor of fractions 564/54, 870/141.
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 564/54,870/141?
Given fractions are 564/54,870/141
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 564/54,870/141, numerators are 564,870
Denominators are 54,141
The GCF of 564,870 is 6 .
LCM of 54,141 is 2538.
The greatest common factor of 564/54,870/141 = [GCF of 564,870]/[LCM of 54,141]= 6/2538
Therefore, the GCF of 564/54,870/141 is 6/2538.
To find the highest common factor of 564,870, we have to find the factors of both numbers and list the highest common factor.
The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
The factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870
The HCF of 564,870 is 6.
Lets's calculate GCF of 564,870
| 2 | 564, 870 |
| 3 | 282, 435 |
| 94, 145 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 564,870 By Matching Biggest Common Factor Method
Now, list down the factors of 564
:1,2,3,4,6,12,47,94,141,188,282,564
Now, list down the factors of 870
:1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870
Greatest Common Factor
We found the factors 564,870 . The biggest common factor number is the GCF number.
So the greatest common factor 564,870 is 6.
Lets's calculate LCM of 54,141
| 3 | 54, 141 |
| 18, 47 |
∴ So the LCM of the given numbers is 3 x 18 x 47 = 2538
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/2538
Therefore, the GCF of Fractions 564/54,870/141 is 6/2538
Least Common Multiple of 54,141 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 54,141 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,141) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(54,141) x common factors =3 x 1 = 3
LCM(54,141) = ( 54 × 141 ) / 3
LCM(54,141) = 7614 / 3
LCM(54,141) = 2538
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FAQs on GCF of Fractions of 564/54, 870/141
1. What is the HCF of 564,870?
The HCF of 564,870 is 6
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 564/54, 870/141?
Answer: GCF of Numerators as per given numbers 564/54, 870/141 is
GCF of Numerators i.e. for 564,870 is 6
LCM of denominators i.e. for 54,141 is 2538.
Thus, GCF of Fractions is 6/2538.Finally, GCF of Fractions for 564/54, 870/141 is 6/2538.