Use our free GCF of Fractions Calculator tool to compute the GCF of 2780/556, 8400/2729 i.e 20/1517324 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2780/556, 8400/2729.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 2780/556,8400/2729
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 2780/556,8400/2729, numerators are 2780,8400
Denominators are 556,2729
The GCF of 2780,8400 is 20 .
LCM of 556,2729 is 1517324.
The greatest common factor of 2780/556,8400/2729 = [GCF of 2780,8400]/[LCM of 556,2729]= 20/1517324
Therefore, the GCF of 2780/556,8400/2729 is 20/1517324.
To find the highest common factor of 2780,8400, we have to find the factors of both numbers and list the highest common factor.
The factors of 2780 are 1, 2, 4, 5, 10, 20, 139, 278, 556, 695, 1390, 2780
The factors of 8400 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 100, 105, 112, 120, 140, 150, 168, 175, 200, 210, 240, 280, 300, 336, 350, 400, 420, 525, 560, 600, 700, 840, 1050, 1200, 1400, 1680, 2100, 2800, 4200, 8400
The HCF of 2780,8400 is 20.
Lets's calculate GCF of 2780,8400
2 | 2780, 8400 |
2 | 1390, 4200 |
5 | 695, 2100 |
139, 420 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Now, list down the factors of 2780
:1,2,4,5,10,20,139,278,556,695,1390,2780
Now, list down the factors of 8400
:1,2,3,4,5,6,7,8,10,12,14,15,16,20,21,24,25,28,30,35,40,42,48,50,56,60,70,75,80,84,100,105,112,120,140,150,168,175,200,210,240,280,300,336,350,400,420,525,560,600,700,840,1050,1200,1400,1680,2100,2800,4200,8400
Greatest Common Factor
We found the factors 2780,8400 . The biggest common factor number is the GCF number.
So the greatest common factor 2780,8400 is 20.
Lets's calculate LCM of 556,2729
Given numbers has no common factors except 1. So, there LCM is their product i.e 1517324
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/1517324
Therefore, the GCF of Fractions 2780/556,8400/2729 is 20/1517324
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 556,2729 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(556,2729) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(556,2729) x common factors =1 x 1 = 1
LCM(556,2729) = ( 556 × 2729 ) / 1
LCM(556,2729) = 1517324 / 1
LCM(556,2729) = 1517324
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 2780,8400?
The HCF of 2780,8400 is 20
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 2780/556, 8400/2729?
Answer: GCF of Numerators as per given numbers 2780/556, 8400/2729 is
GCF of Numerators i.e. for 2780,8400 is 20
LCM of denominators i.e. for 556,2729 is 1517324.
Thus, GCF of Fractions is 20/1517324.Finally, GCF of Fractions for 2780/556, 8400/2729 is 20/1517324.