GCF of 390/414, 698/322
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 390/414, 698/322 i.e 2/2898 easily. The following is the detailed procedure to determine the greatest common factor of fractions 390/414, 698/322.
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 390/414,698/322?
Given fractions are 390/414,698/322
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 390/414,698/322, numerators are 390,698
Denominators are 414,322
The GCF of 390,698 is 2 .
LCM of 414,322 is 2898.
The greatest common factor of 390/414,698/322 = [GCF of 390,698]/[LCM of 414,322]= 2/2898
Therefore, the GCF of 390/414,698/322 is 2/2898.
To find the highest common factor of 390,698, we have to find the factors of both numbers and list the highest common factor.
The factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390
The factors of 698 are 1, 2, 349, 698
The HCF of 390,698 is 2.
Lets's calculate GCF of 390,698
| 2 | 390, 698 |
| 195, 349 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 390,698 By Matching Biggest Common Factor Method
Now, list down the factors of 390
:1,2,3,5,6,10,13,15,26,30,39,65,78,130,195,390
Now, list down the factors of 698
:1,2,349,698
Greatest Common Factor
We found the factors 390,698 . The biggest common factor number is the GCF number.
So the greatest common factor 390,698 is 2.
Lets's calculate LCM of 414,322
| 2 | 414, 322 |
| 23 | 207, 161 |
| 9, 7 |
∴ So the LCM of the given numbers is 2 x 23 x 9 x 7 = 2898
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2898
Therefore, the GCF of Fractions 390/414,698/322 is 2/2898
Least Common Multiple of 414,322 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 414,322 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,322) = 46
common factors(in case of two or more numbers have common factors) = 1
GCF(414,322) x common factors =46 x 1 = 46
LCM(414,322) = ( 414 × 322 ) / 46
LCM(414,322) = 133308 / 46
LCM(414,322) = 2898
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FAQs on GCF of Fractions of 390/414, 698/322
1. What is the HCF of 390,698?
The HCF of 390,698 is 2
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 390/414, 698/322?
Answer: GCF of Numerators as per given numbers 390/414, 698/322 is
GCF of Numerators i.e. for 390,698 is 2
LCM of denominators i.e. for 414,322 is 2898.
Thus, GCF of Fractions is 2/2898.Finally, GCF of Fractions for 390/414, 698/322 is 2/2898.