Use our free GCF of Fractions Calculator tool to compute the GCF of 13/64, 28/92, 420/170 i.e 1/125120 easily. The following is the detailed procedure to determine the greatest common factor of fractions 13/64, 28/92, 420/170.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 13/64,28/92,420/170
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 13/64,28/92,420/170, numerators are 13,28,420
Denominators are 64,92,170
The GCF of 13,28,420 is 1 .
LCM of 64,92,170 is 125120.
The greatest common factor of 13/64,28/92,420/170 = [GCF of 13,28,420]/[LCM of 64,92,170]= 1/125120
Therefore, the GCF of 13/64,28/92,420/170 is 1/125120.
To find the highest common factor of 13,28,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 13 are 1, 13
The factors of 28 are 1, 2, 4, 7, 14, 28
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 13,28,420 is 1.
Lets's calculate GCF of 13,28,420
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 13
:1,13
Now, list down the factors of 28
:1,2,4,7,14,28
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 13,28,420 . The biggest common factor number is the GCF number.
So the greatest common factor 13,28,420 is 1.
Lets's calculate LCM of 64,92,170
2 | 64, 92, 170 |
2 | 32, 46, 85 |
16, 23, 85 |
∴ So the LCM of the given numbers is 2 x 2 x 16 x 23 x 85 = 125120
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/125120
Therefore, the GCF of Fractions 13/64,28/92,420/170 is 1/125120
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 64,92,170 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(64,92,170) = 2
common factors(in case of two or more numbers have common factors) = 4
GCF(64,92,170) x common factors =2 x 4 = 8
LCM(64,92,170) = ( 64 × 92 × 170 ) / 8
LCM(64,92,170) = 1000960 / 8
LCM(64,92,170) = 125120
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 13,28,420?
The HCF of 13,28,420 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 13/64, 28/92, 420/170?
Answer: GCF of Numerators as per given numbers 13/64, 28/92, 420/170 is
GCF of Numerators i.e. for 13,28,420 is 1
LCM of denominators i.e. for 64,92,170 is 125120.
Thus, GCF of Fractions is 1/125120.Finally, GCF of Fractions for 13/64, 28/92, 420/170 is 1/125120.