GCF of 987/454, 231/174
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 987/454, 231/174 i.e 21/39498 easily. The following is the detailed procedure to determine the greatest common factor of fractions 987/454, 231/174.
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 987/454,231/174?
Given fractions are 987/454,231/174
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 987/454,231/174, numerators are 987,231
Denominators are 454,174
The GCF of 987,231 is 21 .
LCM of 454,174 is 39498.
The greatest common factor of 987/454,231/174 = [GCF of 987,231]/[LCM of 454,174]= 21/39498
Therefore, the GCF of 987/454,231/174 is 21/39498.
To find the highest common factor of 987,231, we have to find the factors of both numbers and list the highest common factor.
The factors of 987 are 1, 3, 7, 21, 47, 141, 329, 987
The factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231
The HCF of 987,231 is 21.
Lets's calculate GCF of 987,231
| 3 | 987, 231 |
| 7 | 329, 77 |
| 47, 11 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Greatest Common Factor of 987,231 By Matching Biggest Common Factor Method
Now, list down the factors of 987
:1,3,7,21,47,141,329,987
Now, list down the factors of 231
:1,3,7,11,21,33,77,231
Greatest Common Factor
We found the factors 987,231 . The biggest common factor number is the GCF number.
So the greatest common factor 987,231 is 21.
Lets's calculate LCM of 454,174
| 2 | 454, 174 |
| 227, 87 |
∴ So the LCM of the given numbers is 2 x 227 x 87 = 39498
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/39498
Therefore, the GCF of Fractions 987/454,231/174 is 21/39498
Least Common Multiple of 454,174 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 454,174 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(454,174) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(454,174) x common factors =2 x 1 = 2
LCM(454,174) = ( 454 × 174 ) / 2
LCM(454,174) = 78996 / 2
LCM(454,174) = 39498
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FAQs on GCF of Fractions of 987/454, 231/174
1. What is the HCF of 987,231?
The HCF of 987,231 is 21
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 987/454, 231/174?
Answer: GCF of Numerators as per given numbers 987/454, 231/174 is
GCF of Numerators i.e. for 987,231 is 21
LCM of denominators i.e. for 454,174 is 39498.
Thus, GCF of Fractions is 21/39498.Finally, GCF of Fractions for 987/454, 231/174 is 21/39498.