GCF of 112/24, 756/978
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 112/24, 756/978 i.e 28/3912 easily. The following is the detailed procedure to determine the greatest common factor of fractions 112/24, 756/978.
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 112/24,756/978?
Given fractions are 112/24,756/978
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 112/24,756/978, numerators are 112,756
Denominators are 24,978
The GCF of 112,756 is 28 .
LCM of 24,978 is 3912.
The greatest common factor of 112/24,756/978 = [GCF of 112,756]/[LCM of 24,978]= 28/3912
Therefore, the GCF of 112/24,756/978 is 28/3912.
To find the highest common factor of 112,756, we have to find the factors of both numbers and list the highest common factor.
The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
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 112,756 is 28.
Lets's calculate GCF of 112,756
| 2 | 112, 756 |
| 2 | 56, 378 |
| 7 | 28, 189 |
| 4, 27 |
∴ So the GCF of the given numbers is 2 x 2 x 7 = 28
Greatest Common Factor of 112,756 By Matching Biggest Common Factor Method
Now, list down the factors of 112
:1,2,4,7,8,14,16,28,56,112
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 112,756 . The biggest common factor number is the GCF number.
So the greatest common factor 112,756 is 28.
Lets's calculate LCM of 24,978
| 2 | 24, 978 |
| 3 | 12, 489 |
| 4, 163 |
∴ So the LCM of the given numbers is 2 x 3 x 4 x 163 = 3912
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 28/3912
Therefore, the GCF of Fractions 112/24,756/978 is 28/3912
Least Common Multiple of 24,978 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 24,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(24,978) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(24,978) x common factors =6 x 1 = 6
LCM(24,978) = ( 24 × 978 ) / 6
LCM(24,978) = 23472 / 6
LCM(24,978) = 3912
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FAQs on GCF of Fractions of 112/24, 756/978
1. What is the HCF of 112,756?
The HCF of 112,756 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 112/24, 756/978?
Answer: GCF of Numerators as per given numbers 112/24, 756/978 is
GCF of Numerators i.e. for 112,756 is 28
LCM of denominators i.e. for 24,978 is 3912.
Thus, GCF of Fractions is 28/3912.Finally, GCF of Fractions for 112/24, 756/978 is 28/3912.