Use our free GCF of Fractions Calculator tool to compute the GCF of 520/429, 972/398 i.e 4/170742 easily. The following is the detailed procedure to determine the greatest common factor of fractions 520/429, 972/398.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 520/429,972/398
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 520/429,972/398, numerators are 520,972
Denominators are 429,398
The GCF of 520,972 is 4 .
LCM of 429,398 is 170742.
The greatest common factor of 520/429,972/398 = [GCF of 520,972]/[LCM of 429,398]= 4/170742
Therefore, the GCF of 520/429,972/398 is 4/170742.
To find the highest common factor of 520,972, we have to find the factors of both numbers and list the highest common factor.
The factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520
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 520,972 is 4.
Lets's calculate GCF of 520,972
2 | 520, 972 |
2 | 260, 486 |
130, 243 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 520
:1,2,4,5,8,10,13,20,26,40,52,65,104,130,260,520
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 520,972 . The biggest common factor number is the GCF number.
So the greatest common factor 520,972 is 4.
Lets's calculate LCM of 429,398
Given numbers has no common factors except 1. So, there LCM is their product i.e 170742
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/170742
Therefore, the GCF of Fractions 520/429,972/398 is 4/170742
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 429,398 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(429,398) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(429,398) x common factors =1 x 1 = 1
LCM(429,398) = ( 429 × 398 ) / 1
LCM(429,398) = 170742 / 1
LCM(429,398) = 170742
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 520,972?
The HCF of 520,972 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 520/429, 972/398?
Answer: GCF of Numerators as per given numbers 520/429, 972/398 is
GCF of Numerators i.e. for 520,972 is 4
LCM of denominators i.e. for 429,398 is 170742.
Thus, GCF of Fractions is 4/170742.Finally, GCF of Fractions for 520/429, 972/398 is 4/170742.