Use our free GCF of Fractions Calculator tool to compute the GCF of 512/124, 672/740 i.e 32/22940 easily. The following is the detailed procedure to determine the greatest common factor of fractions 512/124, 672/740.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 512/124,672/740
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 512/124,672/740, numerators are 512,672
Denominators are 124,740
The GCF of 512,672 is 32 .
LCM of 124,740 is 22940.
The greatest common factor of 512/124,672/740 = [GCF of 512,672]/[LCM of 124,740]= 32/22940
Therefore, the GCF of 512/124,672/740 is 32/22940.
To find the highest common factor of 512,672, we have to find the factors of both numbers and list the highest common factor.
The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
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 HCF of 512,672 is 32.
Lets's calculate GCF of 512,672
2 | 512, 672 |
2 | 256, 336 |
2 | 128, 168 |
2 | 64, 84 |
2 | 32, 42 |
16, 21 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32
Now, list down the factors of 512
:1,2,4,8,16,32,64,128,256,512
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
Greatest Common Factor
We found the factors 512,672 . The biggest common factor number is the GCF number.
So the greatest common factor 512,672 is 32.
Lets's calculate LCM of 124,740
2 | 124, 740 |
2 | 62, 370 |
31, 185 |
∴ So the LCM of the given numbers is 2 x 2 x 31 x 185 = 22940
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/22940
Therefore, the GCF of Fractions 512/124,672/740 is 32/22940
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 124,740 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(124,740) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(124,740) x common factors =4 x 1 = 4
LCM(124,740) = ( 124 × 740 ) / 4
LCM(124,740) = 91760 / 4
LCM(124,740) = 22940
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 512,672?
The HCF of 512,672 is 32
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 512/124, 672/740?
Answer: GCF of Numerators as per given numbers 512/124, 672/740 is
GCF of Numerators i.e. for 512,672 is 32
LCM of denominators i.e. for 124,740 is 22940.
Thus, GCF of Fractions is 32/22940.Finally, GCF of Fractions for 512/124, 672/740 is 32/22940.