GCF of 172/48, 198/414
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 172/48, 198/414 i.e 2/3312 easily. The following is the detailed procedure to determine the greatest common factor of fractions 172/48, 198/414.
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 172/48,198/414?
Given fractions are 172/48,198/414
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 172/48,198/414, numerators are 172,198
Denominators are 48,414
The GCF of 172,198 is 2 .
LCM of 48,414 is 3312.
The greatest common factor of 172/48,198/414 = [GCF of 172,198]/[LCM of 48,414]= 2/3312
Therefore, the GCF of 172/48,198/414 is 2/3312.
To find the highest common factor of 172,198, we have to find the factors of both numbers and list the highest common factor.
The factors of 172 are 1, 2, 4, 43, 86, 172
The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198
The HCF of 172,198 is 2.
Lets's calculate GCF of 172,198
| 2 | 172, 198 |
| 86, 99 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 172,198 By Matching Biggest Common Factor Method
Now, list down the factors of 172
:1,2,4,43,86,172
Now, list down the factors of 198
:1,2,3,6,9,11,18,22,33,66,99,198
Greatest Common Factor
We found the factors 172,198 . The biggest common factor number is the GCF number.
So the greatest common factor 172,198 is 2.
Lets's calculate LCM of 48,414
| 2 | 48, 414 |
| 3 | 24, 207 |
| 8, 69 |
∴ So the LCM of the given numbers is 2 x 3 x 8 x 69 = 3312
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/3312
Therefore, the GCF of Fractions 172/48,198/414 is 2/3312
Least Common Multiple of 48,414 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 48,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(48,414) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(48,414) x common factors =6 x 1 = 6
LCM(48,414) = ( 48 × 414 ) / 6
LCM(48,414) = 19872 / 6
LCM(48,414) = 3312
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FAQs on GCF of Fractions of 172/48, 198/414
1. What is the HCF of 172,198?
The HCF of 172,198 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 172/48, 198/414?
Answer: GCF of Numerators as per given numbers 172/48, 198/414 is
GCF of Numerators i.e. for 172,198 is 2
LCM of denominators i.e. for 48,414 is 3312.
Thus, GCF of Fractions is 2/3312.Finally, GCF of Fractions for 172/48, 198/414 is 2/3312.