GCF of 6909/630, 5742/6396
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6909/630, 5742/6396 i.e 3/671580 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6909/630, 5742/6396.
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 6909/630,5742/6396?
Given fractions are 6909/630,5742/6396
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 6909/630,5742/6396, numerators are 6909,5742
Denominators are 630,6396
The GCF of 6909,5742 is 3 .
LCM of 630,6396 is 671580.
The greatest common factor of 6909/630,5742/6396 = [GCF of 6909,5742]/[LCM of 630,6396]= 3/671580
Therefore, the GCF of 6909/630,5742/6396 is 3/671580.
To find the highest common factor of 6909,5742, we have to find the factors of both numbers and list the highest common factor.
The factors of 6909 are 1, 3, 7, 21, 47, 49, 141, 147, 329, 987, 2303, 6909
The factors of 5742 are 1, 2, 3, 6, 9, 11, 18, 22, 29, 33, 58, 66, 87, 99, 174, 198, 261, 319, 522, 638, 957, 1914, 2871, 5742
The HCF of 6909,5742 is 3.
Lets's calculate GCF of 6909,5742
| 3 | 6909, 5742 |
| 2303, 1914 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 6909,5742 By Matching Biggest Common Factor Method
Now, list down the factors of 6909
:1,3,7,21,47,49,141,147,329,987,2303,6909
Now, list down the factors of 5742
:1,2,3,6,9,11,18,22,29,33,58,66,87,99,174,198,261,319,522,638,957,1914,2871,5742
Greatest Common Factor
We found the factors 6909,5742 . The biggest common factor number is the GCF number.
So the greatest common factor 6909,5742 is 3.
Lets's calculate LCM of 630,6396
| 2 | 630, 6396 |
| 3 | 315, 3198 |
| 105, 1066 |
∴ So the LCM of the given numbers is 2 x 3 x 105 x 1066 = 671580
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/671580
Therefore, the GCF of Fractions 6909/630,5742/6396 is 3/671580
Least Common Multiple of 630,6396 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 630,6396 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(630,6396) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(630,6396) x common factors =6 x 1 = 6
LCM(630,6396) = ( 630 × 6396 ) / 6
LCM(630,6396) = 4029480 / 6
LCM(630,6396) = 671580
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FAQs on GCF of Fractions of 6909/630, 5742/6396
1. What is the HCF of 6909,5742?
The HCF of 6909,5742 is 3
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 6909/630, 5742/6396?
Answer: GCF of Numerators as per given numbers 6909/630, 5742/6396 is
GCF of Numerators i.e. for 6909,5742 is 3
LCM of denominators i.e. for 630,6396 is 671580.
Thus, GCF of Fractions is 3/671580.Finally, GCF of Fractions for 6909/630, 5742/6396 is 3/671580.