GCF of 318/34, 312/982
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 318/34, 312/982 i.e 6/16694 easily. The following is the detailed procedure to determine the greatest common factor of fractions 318/34, 312/982.
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 318/34,312/982?
Given fractions are 318/34,312/982
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 318/34,312/982, numerators are 318,312
Denominators are 34,982
The GCF of 318,312 is 6 .
LCM of 34,982 is 16694.
The greatest common factor of 318/34,312/982 = [GCF of 318,312]/[LCM of 34,982]= 6/16694
Therefore, the GCF of 318/34,312/982 is 6/16694.
To find the highest common factor of 318,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 318 are 1, 2, 3, 6, 53, 106, 159, 318
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 318,312 is 6.
Lets's calculate GCF of 318,312
| 2 | 318, 312 |
| 3 | 159, 156 |
| 53, 52 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 318,312 By Matching Biggest Common Factor Method
Now, list down the factors of 318
:1,2,3,6,53,106,159,318
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 318,312 . The biggest common factor number is the GCF number.
So the greatest common factor 318,312 is 6.
Lets's calculate LCM of 34,982
| 2 | 34, 982 |
| 17, 491 |
∴ So the LCM of the given numbers is 2 x 17 x 491 = 16694
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/16694
Therefore, the GCF of Fractions 318/34,312/982 is 6/16694
Least Common Multiple of 34,982 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 34,982 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,982) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(34,982) x common factors =2 x 1 = 2
LCM(34,982) = ( 34 × 982 ) / 2
LCM(34,982) = 33388 / 2
LCM(34,982) = 16694
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FAQs on GCF of Fractions of 318/34, 312/982
1. What is the HCF of 318,312?
The HCF of 318,312 is 6
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 318/34, 312/982?
Answer: GCF of Numerators as per given numbers 318/34, 312/982 is
GCF of Numerators i.e. for 318,312 is 6
LCM of denominators i.e. for 34,982 is 16694.
Thus, GCF of Fractions is 6/16694.Finally, GCF of Fractions for 318/34, 312/982 is 6/16694.