GCF of 1026/321, 9234/207
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1026/321, 9234/207 i.e 1026/22149 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1026/321, 9234/207.
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 1026/321,9234/207?
Given fractions are 1026/321,9234/207
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 1026/321,9234/207, numerators are 1026,9234
Denominators are 321,207
The GCF of 1026,9234 is 1026 .
LCM of 321,207 is 22149.
The greatest common factor of 1026/321,9234/207 = [GCF of 1026,9234]/[LCM of 321,207]= 1026/22149
Therefore, the GCF of 1026/321,9234/207 is 1026/22149.
To find the highest common factor of 1026,9234, we have to find the factors of both numbers and list the highest common factor.
The factors of 1026 are 1, 2, 3, 6, 9, 18, 19, 27, 38, 54, 57, 114, 171, 342, 513, 1026
The factors of 9234 are 1, 2, 3, 6, 9, 18, 19, 27, 38, 54, 57, 81, 114, 162, 171, 243, 342, 486, 513, 1026, 1539, 3078, 4617, 9234
The HCF of 1026,9234 is 1026.
Lets's calculate GCF of 1026,9234
| 2 | 1026, 9234 |
| 3 | 513, 4617 |
| 3 | 171, 1539 |
| 3 | 57, 513 |
| 19 | 19, 171 |
| 1, 9 |
∴ So the GCF of the given numbers is 2 x 3 x 3 x 3 x 19 = 1026
Greatest Common Factor of 1026,9234 By Matching Biggest Common Factor Method
Now, list down the factors of 1026
:1,2,3,6,9,18,19,27,38,54,57,114,171,342,513,1026
Now, list down the factors of 9234
:1,2,3,6,9,18,19,27,38,54,57,81,114,162,171,243,342,486,513,1026,1539,3078,4617,9234
Greatest Common Factor
We found the factors 1026,9234 . The biggest common factor number is the GCF number.
So the greatest common factor 1026,9234 is 1026.
Lets's calculate LCM of 321,207
| 3 | 321, 207 |
| 107, 69 |
∴ So the LCM of the given numbers is 3 x 107 x 69 = 22149
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1026/22149
Therefore, the GCF of Fractions 1026/321,9234/207 is 1026/22149
Least Common Multiple of 321,207 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 321,207 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(321,207) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(321,207) x common factors =3 x 1 = 3
LCM(321,207) = ( 321 × 207 ) / 3
LCM(321,207) = 66447 / 3
LCM(321,207) = 22149
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FAQs on GCF of Fractions of 1026/321, 9234/207
1. What is the HCF of 1026,9234?
The HCF of 1026,9234 is 1026
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 1026/321, 9234/207?
Answer: GCF of Numerators as per given numbers 1026/321, 9234/207 is
GCF of Numerators i.e. for 1026,9234 is 1026
LCM of denominators i.e. for 321,207 is 22149.
Thus, GCF of Fractions is 1026/22149.Finally, GCF of Fractions for 1026/321, 9234/207 is 1026/22149.