Use our free GCF of Fractions Calculator tool to compute the GCF of 320/506, 972/542 i.e 4/137126 easily. The following is the detailed procedure to determine the greatest common factor of fractions 320/506, 972/542.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 320/506,972/542
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 320/506,972/542, numerators are 320,972
Denominators are 506,542
The GCF of 320,972 is 4 .
LCM of 506,542 is 137126.
The greatest common factor of 320/506,972/542 = [GCF of 320,972]/[LCM of 506,542]= 4/137126
Therefore, the GCF of 320/506,972/542 is 4/137126.
To find the highest common factor of 320,972, we have to find the factors of both numbers and list the highest common factor.
The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
The HCF of 320,972 is 4.
Lets's calculate GCF of 320,972
2 | 320, 972 |
2 | 160, 486 |
80, 243 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 320
:1,2,4,5,8,10,16,20,32,40,64,80,160,320
Now, list down the factors of 972
:1,2,3,4,6,9,12,18,27,36,54,81,108,162,243,324,486,972
Greatest Common Factor
We found the factors 320,972 . The biggest common factor number is the GCF number.
So the greatest common factor 320,972 is 4.
Lets's calculate LCM of 506,542
2 | 506, 542 |
253, 271 |
∴ So the LCM of the given numbers is 2 x 253 x 271 = 137126
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/137126
Therefore, the GCF of Fractions 320/506,972/542 is 4/137126
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 506,542 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(506,542) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(506,542) x common factors =2 x 1 = 2
LCM(506,542) = ( 506 × 542 ) / 2
LCM(506,542) = 274252 / 2
LCM(506,542) = 137126
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 320,972?
The HCF of 320,972 is 4
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 320/506, 972/542?
Answer: GCF of Numerators as per given numbers 320/506, 972/542 is
GCF of Numerators i.e. for 320,972 is 4
LCM of denominators i.e. for 506,542 is 137126.
Thus, GCF of Fractions is 4/137126.Finally, GCF of Fractions for 320/506, 972/542 is 4/137126.