GCF of 91/24, 117/48, 214/330
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 91/24, 117/48, 214/330 i.e 1/2640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 91/24, 117/48, 214/330.
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 91/24,117/48,214/330?
Given fractions are 91/24,117/48,214/330
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 91/24,117/48,214/330, numerators are 91,117,214
Denominators are 24,48,330
The GCF of 91,117,214 is 1 .
LCM of 24,48,330 is 2640.
The greatest common factor of 91/24,117/48,214/330 = [GCF of 91,117,214]/[LCM of 24,48,330]= 1/2640
Therefore, the GCF of 91/24,117/48,214/330 is 1/2640.
To find the highest common factor of 91,117,214, we have to find the factors of both numbers and list the highest common factor.
The factors of 91 are 1, 7, 13, 91
The factors of 117 are 1, 3, 9, 13, 39, 117
The factors of 214 are 1, 2, 107, 214
The HCF of 91,117,214 is 1.
Lets's calculate GCF of 91,117,214
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 91,117,214 By Matching Biggest Common Factor Method
Now, list down the factors of 91
:1,7,13,91
Now, list down the factors of 117
:1,3,9,13,39,117
Now, list down the factors of 214
:1,2,107,214
Greatest Common Factor
We found the factors 91,117,214 . The biggest common factor number is the GCF number.
So the greatest common factor 91,117,214 is 1.
Lets's calculate LCM of 24,48,330
| 2 | 24, 48, 330 |
| 2 | 12, 24, 165 |
| 2 | 6, 12, 165 |
| 3 | 3, 6, 165 |
| 1, 2, 55 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 1 x 2 x 55 = 2640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2640
Therefore, the GCF of Fractions 91/24,117/48,214/330 is 1/2640
Least Common Multiple of 24,48,330 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 24,48,330 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(24,48,330) = 6
common factors(in case of two or more numbers have common factors) = 24
GCF(24,48,330) x common factors =6 x 24 = 144
LCM(24,48,330) = ( 24 × 48 × 330 ) / 144
LCM(24,48,330) = 380160 / 144
LCM(24,48,330) = 2640
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FAQs on GCF of Fractions of 91/24, 117/48, 214/330
1. What is the HCF of 91,117,214?
The HCF of 91,117,214 is 1
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 91/24, 117/48, 214/330?
Answer: GCF of Numerators as per given numbers 91/24, 117/48, 214/330 is
GCF of Numerators i.e. for 91,117,214 is 1
LCM of denominators i.e. for 24,48,330 is 2640.
Thus, GCF of Fractions is 1/2640.Finally, GCF of Fractions for 91/24, 117/48, 214/330 is 1/2640.