GCF of 987/42, 312/399
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 987/42, 312/399 i.e 3/798 easily. The following is the detailed procedure to determine the greatest common factor of fractions 987/42, 312/399.
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 987/42,312/399?
Given fractions are 987/42,312/399
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 987/42,312/399, numerators are 987,312
Denominators are 42,399
The GCF of 987,312 is 3 .
LCM of 42,399 is 798.
The greatest common factor of 987/42,312/399 = [GCF of 987,312]/[LCM of 42,399]= 3/798
Therefore, the GCF of 987/42,312/399 is 3/798.
To find the highest common factor of 987,312, 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 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 987,312 is 3.
Lets's calculate GCF of 987,312
| 3 | 987, 312 |
| 329, 104 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 987,312 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 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 987,312 . The biggest common factor number is the GCF number.
So the greatest common factor 987,312 is 3.
Lets's calculate LCM of 42,399
| 3 | 42, 399 |
| 7 | 14, 133 |
| 2, 19 |
∴ So the LCM of the given numbers is 3 x 7 x 2 x 19 = 798
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/798
Therefore, the GCF of Fractions 987/42,312/399 is 3/798
Least Common Multiple of 42,399 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 42,399 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,399) = 21
common factors(in case of two or more numbers have common factors) = 1
GCF(42,399) x common factors =21 x 1 = 21
LCM(42,399) = ( 42 × 399 ) / 21
LCM(42,399) = 16758 / 21
LCM(42,399) = 798
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FAQs on GCF of Fractions of 987/42, 312/399
1. What is the HCF of 987,312?
The HCF of 987,312 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 987/42, 312/399?
Answer: GCF of Numerators as per given numbers 987/42, 312/399 is
GCF of Numerators i.e. for 987,312 is 3
LCM of denominators i.e. for 42,399 is 798.
Thus, GCF of Fractions is 3/798.Finally, GCF of Fractions for 987/42, 312/399 is 3/798.