Use our free GCF of Fractions Calculator tool to compute the GCF of 672/386, 688/116 i.e 16/22388 easily. The following is the detailed procedure to determine the greatest common factor of fractions 672/386, 688/116.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 672/386,688/116
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 672/386,688/116, numerators are 672,688
Denominators are 386,116
The GCF of 672,688 is 16 .
LCM of 386,116 is 22388.
The greatest common factor of 672/386,688/116 = [GCF of 672,688]/[LCM of 386,116]= 16/22388
Therefore, the GCF of 672/386,688/116 is 16/22388.
To find the highest common factor of 672,688, we have to find the factors of both numbers and list the highest common factor.
The factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672
The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
The HCF of 672,688 is 16.
Lets's calculate GCF of 672,688
2 | 672, 688 |
2 | 336, 344 |
2 | 168, 172 |
2 | 84, 86 |
42, 43 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Now, list down the factors of 672
:1,2,3,4,6,7,8,12,14,16,21,24,28,32,42,48,56,84,96,112,168,224,336,672
Now, list down the factors of 688
:1,2,4,8,16,43,86,172,344,688
Greatest Common Factor
We found the factors 672,688 . The biggest common factor number is the GCF number.
So the greatest common factor 672,688 is 16.
Lets's calculate LCM of 386,116
2 | 386, 116 |
193, 58 |
∴ So the LCM of the given numbers is 2 x 193 x 58 = 22388
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/22388
Therefore, the GCF of Fractions 672/386,688/116 is 16/22388
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 386,116 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(386,116) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(386,116) x common factors =2 x 1 = 2
LCM(386,116) = ( 386 × 116 ) / 2
LCM(386,116) = 44776 / 2
LCM(386,116) = 22388
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 672,688?
The HCF of 672,688 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 672/386, 688/116?
Answer: GCF of Numerators as per given numbers 672/386, 688/116 is
GCF of Numerators i.e. for 672,688 is 16
LCM of denominators i.e. for 386,116 is 22388.
Thus, GCF of Fractions is 16/22388.Finally, GCF of Fractions for 672/386, 688/116 is 16/22388.