GCF of 2814/75, 9514/507
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2814/75, 9514/507 i.e 134/12675 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2814/75, 9514/507.
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 2814/75,9514/507?
Given fractions are 2814/75,9514/507
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 2814/75,9514/507, numerators are 2814,9514
Denominators are 75,507
The GCF of 2814,9514 is 134 .
LCM of 75,507 is 12675.
The greatest common factor of 2814/75,9514/507 = [GCF of 2814,9514]/[LCM of 75,507]= 134/12675
Therefore, the GCF of 2814/75,9514/507 is 134/12675.
To find the highest common factor of 2814,9514, we have to find the factors of both numbers and list the highest common factor.
The factors of 2814 are 1, 2, 3, 6, 7, 14, 21, 42, 67, 134, 201, 402, 469, 938, 1407, 2814
The factors of 9514 are 1, 2, 67, 71, 134, 142, 4757, 9514
The HCF of 2814,9514 is 134.
Lets's calculate GCF of 2814,9514
| 2 | 2814, 9514 |
| 67 | 1407, 4757 |
| 21, 71 |
∴ So the GCF of the given numbers is 2 x 67 = 134
Greatest Common Factor of 2814,9514 By Matching Biggest Common Factor Method
Now, list down the factors of 2814
:1,2,3,6,7,14,21,42,67,134,201,402,469,938,1407,2814
Now, list down the factors of 9514
:1,2,67,71,134,142,4757,9514
Greatest Common Factor
We found the factors 2814,9514 . The biggest common factor number is the GCF number.
So the greatest common factor 2814,9514 is 134.
Lets's calculate LCM of 75,507
| 3 | 75, 507 |
| 25, 169 |
∴ So the LCM of the given numbers is 3 x 25 x 169 = 12675
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 134/12675
Therefore, the GCF of Fractions 2814/75,9514/507 is 134/12675
Least Common Multiple of 75,507 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 75,507 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,507) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(75,507) x common factors =3 x 1 = 3
LCM(75,507) = ( 75 × 507 ) / 3
LCM(75,507) = 38025 / 3
LCM(75,507) = 12675
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FAQs on GCF of Fractions of 2814/75, 9514/507
1. What is the HCF of 2814,9514?
The HCF of 2814,9514 is 134
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 2814/75, 9514/507?
Answer: GCF of Numerators as per given numbers 2814/75, 9514/507 is
GCF of Numerators i.e. for 2814,9514 is 134
LCM of denominators i.e. for 75,507 is 12675.
Thus, GCF of Fractions is 134/12675.Finally, GCF of Fractions for 2814/75, 9514/507 is 134/12675.