GCF of 504/74, 112/50, 805/78
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 504/74, 112/50, 805/78 i.e 7/72150 easily. The following is the detailed procedure to determine the greatest common factor of fractions 504/74, 112/50, 805/78.
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 504/74,112/50,805/78?
Given fractions are 504/74,112/50,805/78
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 504/74,112/50,805/78, numerators are 504,112,805
Denominators are 74,50,78
The GCF of 504,112,805 is 7 .
LCM of 74,50,78 is 72150.
The greatest common factor of 504/74,112/50,805/78 = [GCF of 504,112,805]/[LCM of 74,50,78]= 7/72150
Therefore, the GCF of 504/74,112/50,805/78 is 7/72150.
To find the highest common factor of 504,112,805, we have to find the factors of both numbers and list the highest common factor.
The factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504
The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
The factors of 805 are 1, 5, 7, 23, 35, 115, 161, 805
The HCF of 504,112,805 is 7.
Lets's calculate GCF of 504,112,805
| 7 | 504, 112, 805 |
| 72, 16, 115 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 504,112,805 By Matching Biggest Common Factor Method
Now, list down the factors of 504
:1,2,3,4,6,7,8,9,12,14,18,21,24,28,36,42,56,63,72,84,126,168,252,504
Now, list down the factors of 112
:1,2,4,7,8,14,16,28,56,112
Now, list down the factors of 805
:1,5,7,23,35,115,161,805
Greatest Common Factor
We found the factors 504,112,805 . The biggest common factor number is the GCF number.
So the greatest common factor 504,112,805 is 7.
Lets's calculate LCM of 74,50,78
| 2 | 74, 50, 78 |
| 37, 25, 39 |
∴ So the LCM of the given numbers is 2 x 37 x 25 x 39 = 72150
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/72150
Therefore, the GCF of Fractions 504/74,112/50,805/78 is 7/72150
Least Common Multiple of 74,50,78 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 74,50,78 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,50,78) = 2
common factors(in case of two or more numbers have common factors) = 2
GCF(74,50,78) x common factors =2 x 2 = 4
LCM(74,50,78) = ( 74 × 50 × 78 ) / 4
LCM(74,50,78) = 288600 / 4
LCM(74,50,78) = 72150
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FAQs on GCF of Fractions of 504/74, 112/50, 805/78
1. What is the HCF of 504,112,805?
The HCF of 504,112,805 is 7
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 504/74, 112/50, 805/78?
Answer: GCF of Numerators as per given numbers 504/74, 112/50, 805/78 is
GCF of Numerators i.e. for 504,112,805 is 7
LCM of denominators i.e. for 74,50,78 is 72150.
Thus, GCF of Fractions is 7/72150.Finally, GCF of Fractions for 504/74, 112/50, 805/78 is 7/72150.