GCF of 520/69, 810/54, 282/28
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 520/69, 810/54, 282/28 i.e 2/17388 easily. The following is the detailed procedure to determine the greatest common factor of fractions 520/69, 810/54, 282/28.
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 520/69,810/54,282/28?
Given fractions are 520/69,810/54,282/28
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 520/69,810/54,282/28, numerators are 520,810,282
Denominators are 69,54,28
The GCF of 520,810,282 is 2 .
LCM of 69,54,28 is 17388.
The greatest common factor of 520/69,810/54,282/28 = [GCF of 520,810,282]/[LCM of 69,54,28]= 2/17388
Therefore, the GCF of 520/69,810/54,282/28 is 2/17388.
To find the highest common factor of 520,810,282, we have to find the factors of both numbers and list the highest common factor.
The factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520
The factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810
The factors of 282 are 1, 2, 3, 6, 47, 94, 141, 282
The HCF of 520,810,282 is 2.
Lets's calculate GCF of 520,810,282
| 2 | 520, 810, 282 |
| 260, 405, 141 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 520,810,282 By Matching Biggest Common Factor Method
Now, list down the factors of 520
:1,2,4,5,8,10,13,20,26,40,52,65,104,130,260,520
Now, list down the factors of 810
:1,2,3,5,6,9,10,15,18,27,30,45,54,81,90,135,162,270,405,810
Now, list down the factors of 282
:1,2,3,6,47,94,141,282
Greatest Common Factor
We found the factors 520,810,282 . The biggest common factor number is the GCF number.
So the greatest common factor 520,810,282 is 2.
Lets's calculate LCM of 69,54,28
| 2 | 69, 54, 28 |
| 3 | 69, 27, 14 |
| 23, 9, 14 |
∴ So the LCM of the given numbers is 2 x 3 x 23 x 9 x 14 = 17388
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/17388
Therefore, the GCF of Fractions 520/69,810/54,282/28 is 2/17388
Least Common Multiple of 69,54,28 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 69,54,28 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(69,54,28) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(69,54,28) x common factors =1 x 6 = 6
LCM(69,54,28) = ( 69 × 54 × 28 ) / 6
LCM(69,54,28) = 104328 / 6
LCM(69,54,28) = 17388
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FAQs on GCF of Fractions of 520/69, 810/54, 282/28
1. What is the HCF of 520,810,282?
The HCF of 520,810,282 is 2
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 520/69, 810/54, 282/28?
Answer: GCF of Numerators as per given numbers 520/69, 810/54, 282/28 is
GCF of Numerators i.e. for 520,810,282 is 2
LCM of denominators i.e. for 69,54,28 is 17388.
Thus, GCF of Fractions is 2/17388.Finally, GCF of Fractions for 520/69, 810/54, 282/28 is 2/17388.