Use our free GCF of Fractions Calculator tool to compute the GCF of 53/749, 59/746, 780/860 i.e 1/240264220 easily. The following is the detailed procedure to determine the greatest common factor of fractions 53/749, 59/746, 780/860.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 53/749,59/746,780/860
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 53/749,59/746,780/860, numerators are 53,59,780
Denominators are 749,746,860
The GCF of 53,59,780 is 1 .
LCM of 749,746,860 is 240264220.
The greatest common factor of 53/749,59/746,780/860 = [GCF of 53,59,780]/[LCM of 749,746,860]= 1/240264220
Therefore, the GCF of 53/749,59/746,780/860 is 1/240264220.
To find the highest common factor of 53,59,780, we have to find the factors of both numbers and list the highest common factor.
The factors of 53 are 1, 53
The factors of 59 are 1, 59
The factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780
The HCF of 53,59,780 is 1.
Lets's calculate GCF of 53,59,780
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 53
:1,53
Now, list down the factors of 59
:1,59
Now, list down the factors of 780
:1,2,3,4,5,6,10,12,13,15,20,26,30,39,52,60,65,78,130,156,195,260,390,780
Greatest Common Factor
We found the factors 53,59,780 . The biggest common factor number is the GCF number.
So the greatest common factor 53,59,780 is 1.
Lets's calculate LCM of 749,746,860
2 | 749, 746, 860 |
749, 373, 430 |
∴ So the LCM of the given numbers is 2 x 749 x 373 x 430 = 240264220
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/240264220
Therefore, the GCF of Fractions 53/749,59/746,780/860 is 1/240264220
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 749,746,860 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(749,746,860) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(749,746,860) x common factors =1 x 2 = 2
LCM(749,746,860) = ( 749 × 746 × 860 ) / 2
LCM(749,746,860) = 480528440 / 2
LCM(749,746,860) = 240264220
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 53,59,780?
The HCF of 53,59,780 is 1
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 53/749, 59/746, 780/860?
Answer: GCF of Numerators as per given numbers 53/749, 59/746, 780/860 is
GCF of Numerators i.e. for 53,59,780 is 1
LCM of denominators i.e. for 749,746,860 is 240264220.
Thus, GCF of Fractions is 1/240264220.Finally, GCF of Fractions for 53/749, 59/746, 780/860 is 1/240264220.