GCF of 1114/578, 2174/9750
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1114/578, 2174/9750 i.e 2/2817750 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1114/578, 2174/9750.
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 1114/578,2174/9750?
Given fractions are 1114/578,2174/9750
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 1114/578,2174/9750, numerators are 1114,2174
Denominators are 578,9750
The GCF of 1114,2174 is 2 .
LCM of 578,9750 is 2817750.
The greatest common factor of 1114/578,2174/9750 = [GCF of 1114,2174]/[LCM of 578,9750]= 2/2817750
Therefore, the GCF of 1114/578,2174/9750 is 2/2817750.
To find the highest common factor of 1114,2174, we have to find the factors of both numbers and list the highest common factor.
The factors of 1114 are 1, 2, 557, 1114
The factors of 2174 are 1, 2, 1087, 2174
The HCF of 1114,2174 is 2.
Lets's calculate GCF of 1114,2174
| 2 | 1114, 2174 |
| 557, 1087 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1114,2174 By Matching Biggest Common Factor Method
Now, list down the factors of 1114
:1,2,557,1114
Now, list down the factors of 2174
:1,2,1087,2174
Greatest Common Factor
We found the factors 1114,2174 . The biggest common factor number is the GCF number.
So the greatest common factor 1114,2174 is 2.
Lets's calculate LCM of 578,9750
| 2 | 578, 9750 |
| 289, 4875 |
∴ So the LCM of the given numbers is 2 x 289 x 4875 = 2817750
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2817750
Therefore, the GCF of Fractions 1114/578,2174/9750 is 2/2817750
Least Common Multiple of 578,9750 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 578,9750 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(578,9750) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(578,9750) x common factors =2 x 1 = 2
LCM(578,9750) = ( 578 × 9750 ) / 2
LCM(578,9750) = 5635500 / 2
LCM(578,9750) = 2817750
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FAQs on GCF of Fractions of 1114/578, 2174/9750
1. What is the HCF of 1114,2174?
The HCF of 1114,2174 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 1114/578, 2174/9750?
Answer: GCF of Numerators as per given numbers 1114/578, 2174/9750 is
GCF of Numerators i.e. for 1114,2174 is 2
LCM of denominators i.e. for 578,9750 is 2817750.
Thus, GCF of Fractions is 2/2817750.Finally, GCF of Fractions for 1114/578, 2174/9750 is 2/2817750.