Use our free GCF of Fractions Calculator tool to compute the GCF of 504/919, 432/175 i.e 72/160825 easily. The following is the detailed procedure to determine the greatest common factor of fractions 504/919, 432/175.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 504/919,432/175
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 504/919,432/175, numerators are 504,432
Denominators are 919,175
The GCF of 504,432 is 72 .
LCM of 919,175 is 160825.
The greatest common factor of 504/919,432/175 = [GCF of 504,432]/[LCM of 919,175]= 72/160825
Therefore, the GCF of 504/919,432/175 is 72/160825.
To find the highest common factor of 504,432, we have to find the factors of both numbers and list the highest common factor.
The factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504
The factors of 432 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432
The HCF of 504,432 is 72.
Lets's calculate GCF of 504,432
2 | 504, 432 |
2 | 252, 216 |
2 | 126, 108 |
3 | 63, 54 |
3 | 21, 18 |
7, 6 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 x 3 = 72
Now, list down the factors of 504
:1,2,3,4,6,7,8,9,12,14,18,21,24,28,36,42,56,63,72,84,126,168,252,504
Now, list down the factors of 432
:1,2,3,4,6,8,9,12,16,18,24,27,36,48,54,72,108,144,216,432
Greatest Common Factor
We found the factors 504,432 . The biggest common factor number is the GCF number.
So the greatest common factor 504,432 is 72.
Lets's calculate LCM of 919,175
Given numbers has no common factors except 1. So, there LCM is their product i.e 160825
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 72/160825
Therefore, the GCF of Fractions 504/919,432/175 is 72/160825
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 919,175 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(919,175) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(919,175) x common factors =1 x 1 = 1
LCM(919,175) = ( 919 × 175 ) / 1
LCM(919,175) = 160825 / 1
LCM(919,175) = 160825
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 504,432?
The HCF of 504,432 is 72
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 504/919, 432/175?
Answer: GCF of Numerators as per given numbers 504/919, 432/175 is
GCF of Numerators i.e. for 504,432 is 72
LCM of denominators i.e. for 919,175 is 160825.
Thus, GCF of Fractions is 72/160825.Finally, GCF of Fractions for 504/919, 432/175 is 72/160825.