GCF of 717/228, 7728/570
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 717/228, 7728/570 i.e 3/1140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 717/228, 7728/570.
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 717/228,7728/570?
Given fractions are 717/228,7728/570
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 717/228,7728/570, numerators are 717,7728
Denominators are 228,570
The GCF of 717,7728 is 3 .
LCM of 228,570 is 1140.
The greatest common factor of 717/228,7728/570 = [GCF of 717,7728]/[LCM of 228,570]= 3/1140
Therefore, the GCF of 717/228,7728/570 is 3/1140.
To find the highest common factor of 717,7728, we have to find the factors of both numbers and list the highest common factor.
The factors of 717 are 1, 3, 239, 717
The factors of 7728 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 23, 24, 28, 42, 46, 48, 56, 69, 84, 92, 112, 138, 161, 168, 184, 276, 322, 336, 368, 483, 552, 644, 966, 1104, 1288, 1932, 2576, 3864, 7728
The HCF of 717,7728 is 3.
Lets's calculate GCF of 717,7728
| 3 | 717, 7728 |
| 239, 2576 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 717,7728 By Matching Biggest Common Factor Method
Now, list down the factors of 717
:1,3,239,717
Now, list down the factors of 7728
:1,2,3,4,6,7,8,12,14,16,21,23,24,28,42,46,48,56,69,84,92,112,138,161,168,184,276,322,336,368,483,552,644,966,1104,1288,1932,2576,3864,7728
Greatest Common Factor
We found the factors 717,7728 . The biggest common factor number is the GCF number.
So the greatest common factor 717,7728 is 3.
Lets's calculate LCM of 228,570
| 2 | 228, 570 |
| 3 | 114, 285 |
| 19 | 38, 95 |
| 2, 5 |
∴ So the LCM of the given numbers is 2 x 3 x 19 x 2 x 5 = 1140
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1140
Therefore, the GCF of Fractions 717/228,7728/570 is 3/1140
Least Common Multiple of 228,570 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 228,570 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(228,570) = 114
common factors(in case of two or more numbers have common factors) = 1
GCF(228,570) x common factors =114 x 1 = 114
LCM(228,570) = ( 228 × 570 ) / 114
LCM(228,570) = 129960 / 114
LCM(228,570) = 1140
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FAQs on GCF of Fractions of 717/228, 7728/570
1. What is the HCF of 717,7728?
The HCF of 717,7728 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 717/228, 7728/570?
Answer: GCF of Numerators as per given numbers 717/228, 7728/570 is
GCF of Numerators i.e. for 717,7728 is 3
LCM of denominators i.e. for 228,570 is 1140.
Thus, GCF of Fractions is 3/1140.Finally, GCF of Fractions for 717/228, 7728/570 is 3/1140.