Use our free GCF of Fractions Calculator tool to compute the GCF of 55/196, 72/490, 678/160 i.e 1/7840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 55/196, 72/490, 678/160.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 55/196,72/490,678/160
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 55/196,72/490,678/160, numerators are 55,72,678
Denominators are 196,490,160
The GCF of 55,72,678 is 1 .
LCM of 196,490,160 is 7840.
The greatest common factor of 55/196,72/490,678/160 = [GCF of 55,72,678]/[LCM of 196,490,160]= 1/7840
Therefore, the GCF of 55/196,72/490,678/160 is 1/7840.
To find the highest common factor of 55,72,678, we have to find the factors of both numbers and list the highest common factor.
The factors of 55 are 1, 5, 11, 55
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678
The HCF of 55,72,678 is 1.
Lets's calculate GCF of 55,72,678
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 55
:1,5,11,55
Now, list down the factors of 72
:1,2,3,4,6,8,9,12,18,24,36,72
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Greatest Common Factor
We found the factors 55,72,678 . The biggest common factor number is the GCF number.
So the greatest common factor 55,72,678 is 1.
Lets's calculate LCM of 196,490,160
2 | 196, 490, 160 |
2 | 98, 245, 80 |
5 | 49, 245, 40 |
7 | 49, 49, 8 |
7 | 7, 7, 8 |
1, 1, 8 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 7 x 7 x 1 x 1 x 8 = 7840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7840
Therefore, the GCF of Fractions 55/196,72/490,678/160 is 1/7840
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 196,490,160 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(196,490,160) = 2
common factors(in case of two or more numbers have common factors) = 980
GCF(196,490,160) x common factors =2 x 980 = 1960
LCM(196,490,160) = ( 196 × 490 × 160 ) / 1960
LCM(196,490,160) = 15366400 / 1960
LCM(196,490,160) = 7840
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 55,72,678?
The HCF of 55,72,678 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 55/196, 72/490, 678/160?
Answer: GCF of Numerators as per given numbers 55/196, 72/490, 678/160 is
GCF of Numerators i.e. for 55,72,678 is 1
LCM of denominators i.e. for 196,490,160 is 7840.
Thus, GCF of Fractions is 1/7840.Finally, GCF of Fractions for 55/196, 72/490, 678/160 is 1/7840.