GCF of 5310/69, 2214/390
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5310/69, 2214/390 i.e 18/8970 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5310/69, 2214/390.
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 5310/69,2214/390?
Given fractions are 5310/69,2214/390
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 5310/69,2214/390, numerators are 5310,2214
Denominators are 69,390
The GCF of 5310,2214 is 18 .
LCM of 69,390 is 8970.
The greatest common factor of 5310/69,2214/390 = [GCF of 5310,2214]/[LCM of 69,390]= 18/8970
Therefore, the GCF of 5310/69,2214/390 is 18/8970.
To find the highest common factor of 5310,2214, we have to find the factors of both numbers and list the highest common factor.
The factors of 5310 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 59, 90, 118, 177, 295, 354, 531, 590, 885, 1062, 1770, 2655, 5310
The factors of 2214 are 1, 2, 3, 6, 9, 18, 27, 41, 54, 82, 123, 246, 369, 738, 1107, 2214
The HCF of 5310,2214 is 18.
Lets's calculate GCF of 5310,2214
| 2 | 5310, 2214 |
| 3 | 2655, 1107 |
| 3 | 885, 369 |
| 295, 123 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 5310,2214 By Matching Biggest Common Factor Method
Now, list down the factors of 5310
:1,2,3,5,6,9,10,15,18,30,45,59,90,118,177,295,354,531,590,885,1062,1770,2655,5310
Now, list down the factors of 2214
:1,2,3,6,9,18,27,41,54,82,123,246,369,738,1107,2214
Greatest Common Factor
We found the factors 5310,2214 . The biggest common factor number is the GCF number.
So the greatest common factor 5310,2214 is 18.
Lets's calculate LCM of 69,390
| 3 | 69, 390 |
| 23, 130 |
∴ So the LCM of the given numbers is 3 x 23 x 130 = 8970
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/8970
Therefore, the GCF of Fractions 5310/69,2214/390 is 18/8970
Least Common Multiple of 69,390 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 69,390 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(69,390) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(69,390) x common factors =3 x 1 = 3
LCM(69,390) = ( 69 × 390 ) / 3
LCM(69,390) = 26910 / 3
LCM(69,390) = 8970
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FAQs on GCF of Fractions of 5310/69, 2214/390
1. What is the HCF of 5310,2214?
The HCF of 5310,2214 is 18
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 5310/69, 2214/390?
Answer: GCF of Numerators as per given numbers 5310/69, 2214/390 is
GCF of Numerators i.e. for 5310,2214 is 18
LCM of denominators i.e. for 69,390 is 8970.
Thus, GCF of Fractions is 18/8970.Finally, GCF of Fractions for 5310/69, 2214/390 is 18/8970.