GCF of 2814/977, 2680/257
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2814/977, 2680/257 i.e 134/251089 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2814/977, 2680/257.
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 2814/977,2680/257?
Given fractions are 2814/977,2680/257
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 2814/977,2680/257, numerators are 2814,2680
Denominators are 977,257
The GCF of 2814,2680 is 134 .
LCM of 977,257 is 251089.
The greatest common factor of 2814/977,2680/257 = [GCF of 2814,2680]/[LCM of 977,257]= 134/251089
Therefore, the GCF of 2814/977,2680/257 is 134/251089.
To find the highest common factor of 2814,2680, 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 2680 are 1, 2, 4, 5, 8, 10, 20, 40, 67, 134, 268, 335, 536, 670, 1340, 2680
The HCF of 2814,2680 is 134.
Lets's calculate GCF of 2814,2680
| 2 | 2814, 2680 |
| 67 | 1407, 1340 |
| 21, 20 |
∴ So the GCF of the given numbers is 2 x 67 = 134
Greatest Common Factor of 2814,2680 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 2680
:1,2,4,5,8,10,20,40,67,134,268,335,536,670,1340,2680
Greatest Common Factor
We found the factors 2814,2680 . The biggest common factor number is the GCF number.
So the greatest common factor 2814,2680 is 134.
Lets's calculate LCM of 977,257
Given numbers has no common factors except 1. So, there LCM is their product i.e 251089
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 134/251089
Therefore, the GCF of Fractions 2814/977,2680/257 is 134/251089
Least Common Multiple of 977,257 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 977,257 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(977,257) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(977,257) x common factors =1 x 1 = 1
LCM(977,257) = ( 977 × 257 ) / 1
LCM(977,257) = 251089 / 1
LCM(977,257) = 251089
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FAQs on GCF of Fractions of 2814/977, 2680/257
1. What is the HCF of 2814,2680?
The HCF of 2814,2680 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 2814/977, 2680/257?
Answer: GCF of Numerators as per given numbers 2814/977, 2680/257 is
GCF of Numerators i.e. for 2814,2680 is 134
LCM of denominators i.e. for 977,257 is 251089.
Thus, GCF of Fractions is 134/251089.Finally, GCF of Fractions for 2814/977, 2680/257 is 134/251089.