GCF of 987/82, 417/382
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 987/82, 417/382 i.e 3/15662 easily. The following is the detailed procedure to determine the greatest common factor of fractions 987/82, 417/382.
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 987/82,417/382?
Given fractions are 987/82,417/382
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 987/82,417/382, numerators are 987,417
Denominators are 82,382
The GCF of 987,417 is 3 .
LCM of 82,382 is 15662.
The greatest common factor of 987/82,417/382 = [GCF of 987,417]/[LCM of 82,382]= 3/15662
Therefore, the GCF of 987/82,417/382 is 3/15662.
To find the highest common factor of 987,417, 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 417 are 1, 3, 139, 417
The HCF of 987,417 is 3.
Lets's calculate GCF of 987,417
| 3 | 987, 417 |
| 329, 139 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 987,417 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 417
:1,3,139,417
Greatest Common Factor
We found the factors 987,417 . The biggest common factor number is the GCF number.
So the greatest common factor 987,417 is 3.
Lets's calculate LCM of 82,382
| 2 | 82, 382 |
| 41, 191 |
∴ So the LCM of the given numbers is 2 x 41 x 191 = 15662
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/15662
Therefore, the GCF of Fractions 987/82,417/382 is 3/15662
Least Common Multiple of 82,382 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 82,382 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,382) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(82,382) x common factors =2 x 1 = 2
LCM(82,382) = ( 82 × 382 ) / 2
LCM(82,382) = 31324 / 2
LCM(82,382) = 15662
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FAQs on GCF of Fractions of 987/82, 417/382
1. What is the HCF of 987,417?
The HCF of 987,417 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 987/82, 417/382?
Answer: GCF of Numerators as per given numbers 987/82, 417/382 is
GCF of Numerators i.e. for 987,417 is 3
LCM of denominators i.e. for 82,382 is 15662.
Thus, GCF of Fractions is 3/15662.Finally, GCF of Fractions for 987/82, 417/382 is 3/15662.