Use our free GCF of Fractions Calculator tool to compute the GCF of 170/140, 222/980 i.e 2/980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 170/140, 222/980.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 170/140,222/980
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 170/140,222/980, numerators are 170,222
Denominators are 140,980
The GCF of 170,222 is 2 .
LCM of 140,980 is 980.
The greatest common factor of 170/140,222/980 = [GCF of 170,222]/[LCM of 140,980]= 2/980
Therefore, the GCF of 170/140,222/980 is 2/980.
To find the highest common factor of 170,222, we have to find the factors of both numbers and list the highest common factor.
The factors of 170 are 1, 2, 5, 10, 17, 34, 85, 170
The factors of 222 are 1, 2, 3, 6, 37, 74, 111, 222
The HCF of 170,222 is 2.
Lets's calculate GCF of 170,222
2 | 170, 222 |
85, 111 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 170
:1,2,5,10,17,34,85,170
Now, list down the factors of 222
:1,2,3,6,37,74,111,222
Greatest Common Factor
We found the factors 170,222 . The biggest common factor number is the GCF number.
So the greatest common factor 170,222 is 2.
Lets's calculate LCM of 140,980
2 | 140, 980 |
2 | 70, 490 |
5 | 35, 245 |
7 | 7, 49 |
1, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 7 x 1 x 7 = 980
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/980
Therefore, the GCF of Fractions 170/140,222/980 is 2/980
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 140,980 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(140,980) = 140
common factors(in case of two or more numbers have common factors) = 1
GCF(140,980) x common factors =140 x 1 = 140
LCM(140,980) = ( 140 × 980 ) / 140
LCM(140,980) = 137200 / 140
LCM(140,980) = 980
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 170,222?
The HCF of 170,222 is 2
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 170/140, 222/980?
Answer: GCF of Numerators as per given numbers 170/140, 222/980 is
GCF of Numerators i.e. for 170,222 is 2
LCM of denominators i.e. for 140,980 is 980.
Thus, GCF of Fractions is 2/980.Finally, GCF of Fractions for 170/140, 222/980 is 2/980.