GCF of 630/260, 5742/109
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 630/260, 5742/109 i.e 18/28340 easily. The following is the detailed procedure to determine the greatest common factor of fractions 630/260, 5742/109.
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 630/260,5742/109?
Given fractions are 630/260,5742/109
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 630/260,5742/109, numerators are 630,5742
Denominators are 260,109
The GCF of 630,5742 is 18 .
LCM of 260,109 is 28340.
The greatest common factor of 630/260,5742/109 = [GCF of 630,5742]/[LCM of 260,109]= 18/28340
Therefore, the GCF of 630/260,5742/109 is 18/28340.
To find the highest common factor of 630,5742, we have to find the factors of both numbers and list the highest common factor.
The factors of 630 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630
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 630,5742 is 18.
Lets's calculate GCF of 630,5742
| 2 | 630, 5742 |
| 3 | 315, 2871 |
| 3 | 105, 957 |
| 35, 319 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 630,5742 By Matching Biggest Common Factor Method
Now, list down the factors of 630
:1,2,3,5,6,7,9,10,14,15,18,21,30,35,42,45,63,70,90,105,126,210,315,630
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 630,5742 . The biggest common factor number is the GCF number.
So the greatest common factor 630,5742 is 18.
Lets's calculate LCM of 260,109
Given numbers has no common factors except 1. So, there LCM is their product i.e 28340
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/28340
Therefore, the GCF of Fractions 630/260,5742/109 is 18/28340
Least Common Multiple of 260,109 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 260,109 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(260,109) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(260,109) x common factors =1 x 1 = 1
LCM(260,109) = ( 260 × 109 ) / 1
LCM(260,109) = 28340 / 1
LCM(260,109) = 28340
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FAQs on GCF of Fractions of 630/260, 5742/109
1. What is the HCF of 630,5742?
The HCF of 630,5742 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 630/260, 5742/109?
Answer: GCF of Numerators as per given numbers 630/260, 5742/109 is
GCF of Numerators i.e. for 630,5742 is 18
LCM of denominators i.e. for 260,109 is 28340.
Thus, GCF of Fractions is 18/28340.Finally, GCF of Fractions for 630/260, 5742/109 is 18/28340.