GCF of 117/28, 414/850
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 117/28, 414/850 i.e 9/11900 easily. The following is the detailed procedure to determine the greatest common factor of fractions 117/28, 414/850.
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 117/28,414/850?
Given fractions are 117/28,414/850
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 117/28,414/850, numerators are 117,414
Denominators are 28,850
The GCF of 117,414 is 9 .
LCM of 28,850 is 11900.
The greatest common factor of 117/28,414/850 = [GCF of 117,414]/[LCM of 28,850]= 9/11900
Therefore, the GCF of 117/28,414/850 is 9/11900.
To find the highest common factor of 117,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 117 are 1, 3, 9, 13, 39, 117
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 117,414 is 9.
Lets's calculate GCF of 117,414
| 3 | 117, 414 |
| 3 | 39, 138 |
| 13, 46 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 117,414 By Matching Biggest Common Factor Method
Now, list down the factors of 117
:1,3,9,13,39,117
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 117,414 . The biggest common factor number is the GCF number.
So the greatest common factor 117,414 is 9.
Lets's calculate LCM of 28,850
| 2 | 28, 850 |
| 14, 425 |
∴ So the LCM of the given numbers is 2 x 14 x 425 = 11900
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/11900
Therefore, the GCF of Fractions 117/28,414/850 is 9/11900
Least Common Multiple of 28,850 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 28,850 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(28,850) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(28,850) x common factors =2 x 1 = 2
LCM(28,850) = ( 28 × 850 ) / 2
LCM(28,850) = 23800 / 2
LCM(28,850) = 11900
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FAQs on GCF of Fractions of 117/28, 414/850
1. What is the HCF of 117,414?
The HCF of 117,414 is 9
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 117/28, 414/850?
Answer: GCF of Numerators as per given numbers 117/28, 414/850 is
GCF of Numerators i.e. for 117,414 is 9
LCM of denominators i.e. for 28,850 is 11900.
Thus, GCF of Fractions is 9/11900.Finally, GCF of Fractions for 117/28, 414/850 is 9/11900.