GCF of 363/414, 117/867
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 363/414, 117/867 i.e 3/119646 easily. The following is the detailed procedure to determine the greatest common factor of fractions 363/414, 117/867.
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 363/414,117/867?
Given fractions are 363/414,117/867
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 363/414,117/867, numerators are 363,117
Denominators are 414,867
The GCF of 363,117 is 3 .
LCM of 414,867 is 119646.
The greatest common factor of 363/414,117/867 = [GCF of 363,117]/[LCM of 414,867]= 3/119646
Therefore, the GCF of 363/414,117/867 is 3/119646.
To find the highest common factor of 363,117, we have to find the factors of both numbers and list the highest common factor.
The factors of 363 are 1, 3, 11, 33, 121, 363
The factors of 117 are 1, 3, 9, 13, 39, 117
The HCF of 363,117 is 3.
Lets's calculate GCF of 363,117
| 3 | 363, 117 |
| 121, 39 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 363,117 By Matching Biggest Common Factor Method
Now, list down the factors of 363
:1,3,11,33,121,363
Now, list down the factors of 117
:1,3,9,13,39,117
Greatest Common Factor
We found the factors 363,117 . The biggest common factor number is the GCF number.
So the greatest common factor 363,117 is 3.
Lets's calculate LCM of 414,867
| 3 | 414, 867 |
| 138, 289 |
∴ So the LCM of the given numbers is 3 x 138 x 289 = 119646
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/119646
Therefore, the GCF of Fractions 363/414,117/867 is 3/119646
Least Common Multiple of 414,867 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 414,867 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,867) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(414,867) x common factors =3 x 1 = 3
LCM(414,867) = ( 414 × 867 ) / 3
LCM(414,867) = 358938 / 3
LCM(414,867) = 119646
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FAQs on GCF of Fractions of 363/414, 117/867
1. What is the HCF of 363,117?
The HCF of 363,117 is 3
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 363/414, 117/867?
Answer: GCF of Numerators as per given numbers 363/414, 117/867 is
GCF of Numerators i.e. for 363,117 is 3
LCM of denominators i.e. for 414,867 is 119646.
Thus, GCF of Fractions is 3/119646.Finally, GCF of Fractions for 363/414, 117/867 is 3/119646.