GCF of 126/314, 2660/6515
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 126/314, 2660/6515 i.e 14/2045710 easily. The following is the detailed procedure to determine the greatest common factor of fractions 126/314, 2660/6515.
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 126/314,2660/6515?
Given fractions are 126/314,2660/6515
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 126/314,2660/6515, numerators are 126,2660
Denominators are 314,6515
The GCF of 126,2660 is 14 .
LCM of 314,6515 is 2045710.
The greatest common factor of 126/314,2660/6515 = [GCF of 126,2660]/[LCM of 314,6515]= 14/2045710
Therefore, the GCF of 126/314,2660/6515 is 14/2045710.
To find the highest common factor of 126,2660, we have to find the factors of both numbers and list the highest common factor.
The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
The factors of 2660 are 1, 2, 4, 5, 7, 10, 14, 19, 20, 28, 35, 38, 70, 76, 95, 133, 140, 190, 266, 380, 532, 665, 1330, 2660
The HCF of 126,2660 is 14.
Lets's calculate GCF of 126,2660
| 2 | 126, 2660 |
| 7 | 63, 1330 |
| 9, 190 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 126,2660 By Matching Biggest Common Factor Method
Now, list down the factors of 126
:1,2,3,6,7,9,14,18,21,42,63,126
Now, list down the factors of 2660
:1,2,4,5,7,10,14,19,20,28,35,38,70,76,95,133,140,190,266,380,532,665,1330,2660
Greatest Common Factor
We found the factors 126,2660 . The biggest common factor number is the GCF number.
So the greatest common factor 126,2660 is 14.
Lets's calculate LCM of 314,6515
Given numbers has no common factors except 1. So, there LCM is their product i.e 2045710
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/2045710
Therefore, the GCF of Fractions 126/314,2660/6515 is 14/2045710
Least Common Multiple of 314,6515 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 314,6515 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(314,6515) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(314,6515) x common factors =1 x 1 = 1
LCM(314,6515) = ( 314 × 6515 ) / 1
LCM(314,6515) = 2045710 / 1
LCM(314,6515) = 2045710
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FAQs on GCF of Fractions of 126/314, 2660/6515
1. What is the HCF of 126,2660?
The HCF of 126,2660 is 14
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 126/314, 2660/6515?
Answer: GCF of Numerators as per given numbers 126/314, 2660/6515 is
GCF of Numerators i.e. for 126,2660 is 14
LCM of denominators i.e. for 314,6515 is 2045710.
Thus, GCF of Fractions is 14/2045710.Finally, GCF of Fractions for 126/314, 2660/6515 is 14/2045710.