GCF of 1314/491, 7000/7261
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1314/491, 7000/7261 i.e 2/3565151 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1314/491, 7000/7261.
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 1314/491,7000/7261?
Given fractions are 1314/491,7000/7261
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 1314/491,7000/7261, numerators are 1314,7000
Denominators are 491,7261
The GCF of 1314,7000 is 2 .
LCM of 491,7261 is 3565151.
The greatest common factor of 1314/491,7000/7261 = [GCF of 1314,7000]/[LCM of 491,7261]= 2/3565151
Therefore, the GCF of 1314/491,7000/7261 is 2/3565151.
To find the highest common factor of 1314,7000, we have to find the factors of both numbers and list the highest common factor.
The factors of 1314 are 1, 2, 3, 6, 9, 18, 73, 146, 219, 438, 657, 1314
The factors of 7000 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 125, 140, 175, 200, 250, 280, 350, 500, 700, 875, 1000, 1400, 1750, 3500, 7000
The HCF of 1314,7000 is 2.
Lets's calculate GCF of 1314,7000
| 2 | 1314, 7000 |
| 657, 3500 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1314,7000 By Matching Biggest Common Factor Method
Now, list down the factors of 1314
:1,2,3,6,9,18,73,146,219,438,657,1314
Now, list down the factors of 7000
:1,2,4,5,7,8,10,14,20,25,28,35,40,50,56,70,100,125,140,175,200,250,280,350,500,700,875,1000,1400,1750,3500,7000
Greatest Common Factor
We found the factors 1314,7000 . The biggest common factor number is the GCF number.
So the greatest common factor 1314,7000 is 2.
Lets's calculate LCM of 491,7261
Given numbers has no common factors except 1. So, there LCM is their product i.e 3565151
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/3565151
Therefore, the GCF of Fractions 1314/491,7000/7261 is 2/3565151
Least Common Multiple of 491,7261 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 491,7261 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(491,7261) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(491,7261) x common factors =1 x 1 = 1
LCM(491,7261) = ( 491 × 7261 ) / 1
LCM(491,7261) = 3565151 / 1
LCM(491,7261) = 3565151
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FAQs on GCF of Fractions of 1314/491, 7000/7261
1. What is the HCF of 1314,7000?
The HCF of 1314,7000 is 2
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 1314/491, 7000/7261?
Answer: GCF of Numerators as per given numbers 1314/491, 7000/7261 is
GCF of Numerators i.e. for 1314,7000 is 2
LCM of denominators i.e. for 491,7261 is 3565151.
Thus, GCF of Fractions is 2/3565151.Finally, GCF of Fractions for 1314/491, 7000/7261 is 2/3565151.