GCF of 987/674, 658/400
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 987/674, 658/400 i.e 329/134800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 987/674, 658/400.
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 987/674,658/400?
Given fractions are 987/674,658/400
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 987/674,658/400, numerators are 987,658
Denominators are 674,400
The GCF of 987,658 is 329 .
LCM of 674,400 is 134800.
The greatest common factor of 987/674,658/400 = [GCF of 987,658]/[LCM of 674,400]= 329/134800
Therefore, the GCF of 987/674,658/400 is 329/134800.
To find the highest common factor of 987,658, 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 658 are 1, 2, 7, 14, 47, 94, 329, 658
The HCF of 987,658 is 329.
Lets's calculate GCF of 987,658
| 7 | 987, 658 |
| 47 | 141, 94 |
| 3, 2 |
∴ So the GCF of the given numbers is 7 x 47 = 329
Greatest Common Factor of 987,658 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 658
:1,2,7,14,47,94,329,658
Greatest Common Factor
We found the factors 987,658 . The biggest common factor number is the GCF number.
So the greatest common factor 987,658 is 329.
Lets's calculate LCM of 674,400
| 2 | 674, 400 |
| 337, 200 |
∴ So the LCM of the given numbers is 2 x 337 x 200 = 134800
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 329/134800
Therefore, the GCF of Fractions 987/674,658/400 is 329/134800
Least Common Multiple of 674,400 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 674,400 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(674,400) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(674,400) x common factors =2 x 1 = 2
LCM(674,400) = ( 674 × 400 ) / 2
LCM(674,400) = 269600 / 2
LCM(674,400) = 134800
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FAQs on GCF of Fractions of 987/674, 658/400
1. What is the HCF of 987,658?
The HCF of 987,658 is 329
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 987/674, 658/400?
Answer: GCF of Numerators as per given numbers 987/674, 658/400 is
GCF of Numerators i.e. for 987,658 is 329
LCM of denominators i.e. for 674,400 is 134800.
Thus, GCF of Fractions is 329/134800.Finally, GCF of Fractions for 987/674, 658/400 is 329/134800.