GCF of 756/12, 560/351
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 756/12, 560/351 i.e 28/1404 easily. The following is the detailed procedure to determine the greatest common factor of fractions 756/12, 560/351.
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 756/12,560/351?
Given fractions are 756/12,560/351
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 756/12,560/351, numerators are 756,560
Denominators are 12,351
The GCF of 756,560 is 28 .
LCM of 12,351 is 1404.
The greatest common factor of 756/12,560/351 = [GCF of 756,560]/[LCM of 12,351]= 28/1404
Therefore, the GCF of 756/12,560/351 is 28/1404.
To find the highest common factor of 756,560, we have to find the factors of both numbers and list the highest common factor.
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 factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560
The HCF of 756,560 is 28.
Lets's calculate GCF of 756,560
| 2 | 756, 560 |
| 2 | 378, 280 |
| 7 | 189, 140 |
| 27, 20 |
∴ So the GCF of the given numbers is 2 x 2 x 7 = 28
Greatest Common Factor of 756,560 By Matching Biggest Common Factor Method
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
Now, list down the factors of 560
:1,2,4,5,7,8,10,14,16,20,28,35,40,56,70,80,112,140,280,560
Greatest Common Factor
We found the factors 756,560 . The biggest common factor number is the GCF number.
So the greatest common factor 756,560 is 28.
Lets's calculate LCM of 12,351
| 3 | 12, 351 |
| 4, 117 |
∴ So the LCM of the given numbers is 3 x 4 x 117 = 1404
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 28/1404
Therefore, the GCF of Fractions 756/12,560/351 is 28/1404
Least Common Multiple of 12,351 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 12,351 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,351) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(12,351) x common factors =3 x 1 = 3
LCM(12,351) = ( 12 × 351 ) / 3
LCM(12,351) = 4212 / 3
LCM(12,351) = 1404
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FAQs on GCF of Fractions of 756/12, 560/351
1. What is the HCF of 756,560?
The HCF of 756,560 is 28
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 756/12, 560/351?
Answer: GCF of Numerators as per given numbers 756/12, 560/351 is
GCF of Numerators i.e. for 756,560 is 28
LCM of denominators i.e. for 12,351 is 1404.
Thus, GCF of Fractions is 28/1404.Finally, GCF of Fractions for 756/12, 560/351 is 28/1404.