Use our free GCF of Fractions Calculator tool to compute the GCF of 712/100, 688/167 i.e 8/16700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 712/100, 688/167.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 712/100,688/167
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 712/100,688/167, numerators are 712,688
Denominators are 100,167
The GCF of 712,688 is 8 .
LCM of 100,167 is 16700.
The greatest common factor of 712/100,688/167 = [GCF of 712,688]/[LCM of 100,167]= 8/16700
Therefore, the GCF of 712/100,688/167 is 8/16700.
To find the highest common factor of 712,688, we have to find the factors of both numbers and list the highest common factor.
The factors of 712 are 1, 2, 4, 8, 89, 178, 356, 712
The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
The HCF of 712,688 is 8.
Lets's calculate GCF of 712,688
2 | 712, 688 |
2 | 356, 344 |
2 | 178, 172 |
89, 86 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Now, list down the factors of 712
:1,2,4,8,89,178,356,712
Now, list down the factors of 688
:1,2,4,8,16,43,86,172,344,688
Greatest Common Factor
We found the factors 712,688 . The biggest common factor number is the GCF number.
So the greatest common factor 712,688 is 8.
Lets's calculate LCM of 100,167
Given numbers has no common factors except 1. So, there LCM is their product i.e 16700
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/16700
Therefore, the GCF of Fractions 712/100,688/167 is 8/16700
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 100,167 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(100,167) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(100,167) x common factors =1 x 1 = 1
LCM(100,167) = ( 100 × 167 ) / 1
LCM(100,167) = 16700 / 1
LCM(100,167) = 16700
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 712,688?
The HCF of 712,688 is 8
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 712/100, 688/167?
Answer: GCF of Numerators as per given numbers 712/100, 688/167 is
GCF of Numerators i.e. for 712,688 is 8
LCM of denominators i.e. for 100,167 is 16700.
Thus, GCF of Fractions is 8/16700.Finally, GCF of Fractions for 712/100, 688/167 is 8/16700.