GCF of 508/32, 554/27, 216/260
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 508/32, 554/27, 216/260 i.e 2/56160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 508/32, 554/27, 216/260.
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 508/32,554/27,216/260?
Given fractions are 508/32,554/27,216/260
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 508/32,554/27,216/260, numerators are 508,554,216
Denominators are 32,27,260
The GCF of 508,554,216 is 2 .
LCM of 32,27,260 is 56160.
The greatest common factor of 508/32,554/27,216/260 = [GCF of 508,554,216]/[LCM of 32,27,260]= 2/56160
Therefore, the GCF of 508/32,554/27,216/260 is 2/56160.
To find the highest common factor of 508,554,216, we have to find the factors of both numbers and list the highest common factor.
The factors of 508 are 1, 2, 4, 127, 254, 508
The factors of 554 are 1, 2, 277, 554
The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
The HCF of 508,554,216 is 2.
Lets's calculate GCF of 508,554,216
| 2 | 508, 554, 216 |
| 254, 277, 108 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 508,554,216 By Matching Biggest Common Factor Method
Now, list down the factors of 508
:1,2,4,127,254,508
Now, list down the factors of 554
:1,2,277,554
Now, list down the factors of 216
:1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216
Greatest Common Factor
We found the factors 508,554,216 . The biggest common factor number is the GCF number.
So the greatest common factor 508,554,216 is 2.
Lets's calculate LCM of 32,27,260
| 2 | 32, 27, 260 |
| 2 | 16, 27, 130 |
| 8, 27, 65 |
∴ So the LCM of the given numbers is 2 x 2 x 8 x 27 x 65 = 56160
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/56160
Therefore, the GCF of Fractions 508/32,554/27,216/260 is 2/56160
Least Common Multiple of 32,27,260 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 32,27,260 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,27,260) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(32,27,260) x common factors =1 x 4 = 4
LCM(32,27,260) = ( 32 × 27 × 260 ) / 4
LCM(32,27,260) = 224640 / 4
LCM(32,27,260) = 56160
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FAQs on GCF of Fractions of 508/32, 554/27, 216/260
1. What is the HCF of 508,554,216?
The HCF of 508,554,216 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 508/32, 554/27, 216/260?
Answer: GCF of Numerators as per given numbers 508/32, 554/27, 216/260 is
GCF of Numerators i.e. for 508,554,216 is 2
LCM of denominators i.e. for 32,27,260 is 56160.
Thus, GCF of Fractions is 2/56160.Finally, GCF of Fractions for 508/32, 554/27, 216/260 is 2/56160.