GCF of 78/884, 204/119, 112/252
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 78/884, 204/119, 112/252 i.e 2/55692 easily. The following is the detailed procedure to determine the greatest common factor of fractions 78/884, 204/119, 112/252.
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 78/884,204/119,112/252?
Given fractions are 78/884,204/119,112/252
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 78/884,204/119,112/252, numerators are 78,204,112
Denominators are 884,119,252
The GCF of 78,204,112 is 2 .
LCM of 884,119,252 is 55692.
The greatest common factor of 78/884,204/119,112/252 = [GCF of 78,204,112]/[LCM of 884,119,252]= 2/55692
Therefore, the GCF of 78/884,204/119,112/252 is 2/55692.
To find the highest common factor of 78,204,112, we have to find the factors of both numbers and list the highest common factor.
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
The factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
The HCF of 78,204,112 is 2.
Lets's calculate GCF of 78,204,112
| 2 | 78, 204, 112 |
| 39, 102, 56 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 78,204,112 By Matching Biggest Common Factor Method
Now, list down the factors of 78
:1,2,3,6,13,26,39,78
Now, list down the factors of 204
:1,2,3,4,6,12,17,34,51,68,102,204
Now, list down the factors of 112
:1,2,4,7,8,14,16,28,56,112
Greatest Common Factor
We found the factors 78,204,112 . The biggest common factor number is the GCF number.
So the greatest common factor 78,204,112 is 2.
Lets's calculate LCM of 884,119,252
| 2 | 884, 119, 252 |
| 2 | 442, 119, 126 |
| 7 | 221, 119, 63 |
| 17 | 221, 17, 9 |
| 13, 1, 9 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 17 x 13 x 1 x 9 = 55692
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/55692
Therefore, the GCF of Fractions 78/884,204/119,112/252 is 2/55692
Least Common Multiple of 884,119,252 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 884,119,252 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(884,119,252) = 1
common factors(in case of two or more numbers have common factors) = 476
GCF(884,119,252) x common factors =1 x 476 = 476
LCM(884,119,252) = ( 884 × 119 × 252 ) / 476
LCM(884,119,252) = 26509392 / 476
LCM(884,119,252) = 55692
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FAQs on GCF of Fractions of 78/884, 204/119, 112/252
1. What is the HCF of 78,204,112?
The HCF of 78,204,112 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 78/884, 204/119, 112/252?
Answer: GCF of Numerators as per given numbers 78/884, 204/119, 112/252 is
GCF of Numerators i.e. for 78,204,112 is 2
LCM of denominators i.e. for 884,119,252 is 55692.
Thus, GCF of Fractions is 2/55692.Finally, GCF of Fractions for 78/884, 204/119, 112/252 is 2/55692.