GCF of 234/31, 117/4688
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 234/31, 117/4688 i.e 117/145328 easily. The following is the detailed procedure to determine the greatest common factor of fractions 234/31, 117/4688.
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 234/31,117/4688?
Given fractions are 234/31,117/4688
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 234/31,117/4688, numerators are 234,117
Denominators are 31,4688
The GCF of 234,117 is 117 .
LCM of 31,4688 is 145328.
The greatest common factor of 234/31,117/4688 = [GCF of 234,117]/[LCM of 31,4688]= 117/145328
Therefore, the GCF of 234/31,117/4688 is 117/145328.
To find the highest common factor of 234,117, we have to find the factors of both numbers and list the highest common factor.
The factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234
The factors of 117 are 1, 3, 9, 13, 39, 117
The HCF of 234,117 is 117.
Lets's calculate GCF of 234,117
| 3 | 234, 117 |
| 3 | 78, 39 |
| 13 | 26, 13 |
| 2, 1 |
∴ So the GCF of the given numbers is 3 x 3 x 13 = 117
Greatest Common Factor of 234,117 By Matching Biggest Common Factor Method
Now, list down the factors of 234
:1,2,3,6,9,13,18,26,39,78,117,234
Now, list down the factors of 117
:1,3,9,13,39,117
Greatest Common Factor
We found the factors 234,117 . The biggest common factor number is the GCF number.
So the greatest common factor 234,117 is 117.
Lets's calculate LCM of 31,4688
Given numbers has no common factors except 1. So, there LCM is their product i.e 145328
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 117/145328
Therefore, the GCF of Fractions 234/31,117/4688 is 117/145328
Least Common Multiple of 31,4688 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 31,4688 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,4688) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(31,4688) x common factors =1 x 1 = 1
LCM(31,4688) = ( 31 × 4688 ) / 1
LCM(31,4688) = 145328 / 1
LCM(31,4688) = 145328
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FAQs on GCF of Fractions of 234/31, 117/4688
1. What is the HCF of 234,117?
The HCF of 234,117 is 117
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 234/31, 117/4688?
Answer: GCF of Numerators as per given numbers 234/31, 117/4688 is
GCF of Numerators i.e. for 234,117 is 117
LCM of denominators i.e. for 31,4688 is 145328.
Thus, GCF of Fractions is 117/145328.Finally, GCF of Fractions for 234/31, 117/4688 is 117/145328.