GCF of 2414/675, 1212/3100
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2414/675, 1212/3100 i.e 2/83700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2414/675, 1212/3100.
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 2414/675,1212/3100?
Given fractions are 2414/675,1212/3100
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 2414/675,1212/3100, numerators are 2414,1212
Denominators are 675,3100
The GCF of 2414,1212 is 2 .
LCM of 675,3100 is 83700.
The greatest common factor of 2414/675,1212/3100 = [GCF of 2414,1212]/[LCM of 675,3100]= 2/83700
Therefore, the GCF of 2414/675,1212/3100 is 2/83700.
To find the highest common factor of 2414,1212, we have to find the factors of both numbers and list the highest common factor.
The factors of 2414 are 1, 2, 17, 34, 71, 142, 1207, 2414
The factors of 1212 are 1, 2, 3, 4, 6, 12, 101, 202, 303, 404, 606, 1212
The HCF of 2414,1212 is 2.
Lets's calculate GCF of 2414,1212
| 2 | 2414, 1212 |
| 1207, 606 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 2414,1212 By Matching Biggest Common Factor Method
Now, list down the factors of 2414
:1,2,17,34,71,142,1207,2414
Now, list down the factors of 1212
:1,2,3,4,6,12,101,202,303,404,606,1212
Greatest Common Factor
We found the factors 2414,1212 . The biggest common factor number is the GCF number.
So the greatest common factor 2414,1212 is 2.
Lets's calculate LCM of 675,3100
| 5 | 675, 3100 |
| 5 | 135, 620 |
| 27, 124 |
∴ So the LCM of the given numbers is 5 x 5 x 27 x 124 = 83700
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/83700
Therefore, the GCF of Fractions 2414/675,1212/3100 is 2/83700
Least Common Multiple of 675,3100 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 675,3100 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(675,3100) = 25
common factors(in case of two or more numbers have common factors) = 1
GCF(675,3100) x common factors =25 x 1 = 25
LCM(675,3100) = ( 675 × 3100 ) / 25
LCM(675,3100) = 2092500 / 25
LCM(675,3100) = 83700
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FAQs on GCF of Fractions of 2414/675, 1212/3100
1. What is the HCF of 2414,1212?
The HCF of 2414,1212 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 2414/675, 1212/3100?
Answer: GCF of Numerators as per given numbers 2414/675, 1212/3100 is
GCF of Numerators i.e. for 2414,1212 is 2
LCM of denominators i.e. for 675,3100 is 83700.
Thus, GCF of Fractions is 2/83700.Finally, GCF of Fractions for 2414/675, 1212/3100 is 2/83700.