Use our free GCF of Fractions Calculator tool to compute the GCF of 688/516, 272/221 i.e 16/114036 easily. The following is the detailed procedure to determine the greatest common factor of fractions 688/516, 272/221.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 688/516,272/221
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 688/516,272/221, numerators are 688,272
Denominators are 516,221
The GCF of 688,272 is 16 .
LCM of 516,221 is 114036.
The greatest common factor of 688/516,272/221 = [GCF of 688,272]/[LCM of 516,221]= 16/114036
Therefore, the GCF of 688/516,272/221 is 16/114036.
To find the highest common factor of 688,272, we have to find the factors of both numbers and list the highest common factor.
The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
The factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272
The HCF of 688,272 is 16.
Lets's calculate GCF of 688,272
2 | 688, 272 |
2 | 344, 136 |
2 | 172, 68 |
2 | 86, 34 |
43, 17 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Now, list down the factors of 688
:1,2,4,8,16,43,86,172,344,688
Now, list down the factors of 272
:1,2,4,8,16,17,34,68,136,272
Greatest Common Factor
We found the factors 688,272 . The biggest common factor number is the GCF number.
So the greatest common factor 688,272 is 16.
Lets's calculate LCM of 516,221
Given numbers has no common factors except 1. So, there LCM is their product i.e 114036
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/114036
Therefore, the GCF of Fractions 688/516,272/221 is 16/114036
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 516,221 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(516,221) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(516,221) x common factors =1 x 1 = 1
LCM(516,221) = ( 516 × 221 ) / 1
LCM(516,221) = 114036 / 1
LCM(516,221) = 114036
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 688,272?
The HCF of 688,272 is 16
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 688/516, 272/221?
Answer: GCF of Numerators as per given numbers 688/516, 272/221 is
GCF of Numerators i.e. for 688,272 is 16
LCM of denominators i.e. for 516,221 is 114036.
Thus, GCF of Fractions is 16/114036.Finally, GCF of Fractions for 688/516, 272/221 is 16/114036.