GCF of 567/404, 756/542
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 567/404, 756/542 i.e 189/109484 easily. The following is the detailed procedure to determine the greatest common factor of fractions 567/404, 756/542.
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 567/404,756/542?
Given fractions are 567/404,756/542
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 567/404,756/542, numerators are 567,756
Denominators are 404,542
The GCF of 567,756 is 189 .
LCM of 404,542 is 109484.
The greatest common factor of 567/404,756/542 = [GCF of 567,756]/[LCM of 404,542]= 189/109484
Therefore, the GCF of 567/404,756/542 is 189/109484.
To find the highest common factor of 567,756, we have to find the factors of both numbers and list the highest common factor.
The factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567
The factors of 756 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756
The HCF of 567,756 is 189.
Lets's calculate GCF of 567,756
| 3 | 567, 756 |
| 3 | 189, 252 |
| 3 | 63, 84 |
| 7 | 21, 28 |
| 3, 4 |
∴ So the GCF of the given numbers is 3 x 3 x 3 x 7 = 189
Greatest Common Factor of 567,756 By Matching Biggest Common Factor Method
Now, list down the factors of 567
:1,3,7,9,21,27,63,81,189,567
Now, list down the factors of 756
:1,2,3,4,6,7,9,12,14,18,21,27,28,36,42,54,63,84,108,126,189,252,378,756
Greatest Common Factor
We found the factors 567,756 . The biggest common factor number is the GCF number.
So the greatest common factor 567,756 is 189.
Lets's calculate LCM of 404,542
| 2 | 404, 542 |
| 202, 271 |
∴ So the LCM of the given numbers is 2 x 202 x 271 = 109484
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 189/109484
Therefore, the GCF of Fractions 567/404,756/542 is 189/109484
Least Common Multiple of 404,542 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 404,542 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(404,542) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(404,542) x common factors =2 x 1 = 2
LCM(404,542) = ( 404 × 542 ) / 2
LCM(404,542) = 218968 / 2
LCM(404,542) = 109484
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FAQs on GCF of Fractions of 567/404, 756/542
1. What is the HCF of 567,756?
The HCF of 567,756 is 189
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 567/404, 756/542?
Answer: GCF of Numerators as per given numbers 567/404, 756/542 is
GCF of Numerators i.e. for 567,756 is 189
LCM of denominators i.e. for 404,542 is 109484.
Thus, GCF of Fractions is 189/109484.Finally, GCF of Fractions for 567/404, 756/542 is 189/109484.