GCF of 690/353, 7314/324
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 690/353, 7314/324 i.e 138/114372 easily. The following is the detailed procedure to determine the greatest common factor of fractions 690/353, 7314/324.
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 690/353,7314/324?
Given fractions are 690/353,7314/324
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 690/353,7314/324, numerators are 690,7314
Denominators are 353,324
The GCF of 690,7314 is 138 .
LCM of 353,324 is 114372.
The greatest common factor of 690/353,7314/324 = [GCF of 690,7314]/[LCM of 353,324]= 138/114372
Therefore, the GCF of 690/353,7314/324 is 138/114372.
To find the highest common factor of 690,7314, we have to find the factors of both numbers and list the highest common factor.
The factors of 690 are 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690
The factors of 7314 are 1, 2, 3, 6, 23, 46, 53, 69, 106, 138, 159, 318, 1219, 2438, 3657, 7314
The HCF of 690,7314 is 138.
Lets's calculate GCF of 690,7314
| 2 | 690, 7314 |
| 3 | 345, 3657 |
| 23 | 115, 1219 |
| 5, 53 |
∴ So the GCF of the given numbers is 2 x 3 x 23 = 138
Greatest Common Factor of 690,7314 By Matching Biggest Common Factor Method
Now, list down the factors of 690
:1,2,3,5,6,10,15,23,30,46,69,115,138,230,345,690
Now, list down the factors of 7314
:1,2,3,6,23,46,53,69,106,138,159,318,1219,2438,3657,7314
Greatest Common Factor
We found the factors 690,7314 . The biggest common factor number is the GCF number.
So the greatest common factor 690,7314 is 138.
Lets's calculate LCM of 353,324
Given numbers has no common factors except 1. So, there LCM is their product i.e 114372
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 138/114372
Therefore, the GCF of Fractions 690/353,7314/324 is 138/114372
Least Common Multiple of 353,324 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 353,324 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(353,324) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(353,324) x common factors =1 x 1 = 1
LCM(353,324) = ( 353 × 324 ) / 1
LCM(353,324) = 114372 / 1
LCM(353,324) = 114372
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FAQs on GCF of Fractions of 690/353, 7314/324
1. What is the HCF of 690,7314?
The HCF of 690,7314 is 138
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 690/353, 7314/324?
Answer: GCF of Numerators as per given numbers 690/353, 7314/324 is
GCF of Numerators i.e. for 690,7314 is 138
LCM of denominators i.e. for 353,324 is 114372.
Thus, GCF of Fractions is 138/114372.Finally, GCF of Fractions for 690/353, 7314/324 is 138/114372.