GCF of 7533/120, 4712/2994
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7533/120, 4712/2994 i.e 31/59880 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7533/120, 4712/2994.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 7533/120,4712/2994?
Given fractions are 7533/120,4712/2994
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 7533/120,4712/2994, numerators are 7533,4712
Denominators are 120,2994
The GCF of 7533,4712 is 31 .
LCM of 120,2994 is 59880.
The greatest common factor of 7533/120,4712/2994 = [GCF of 7533,4712]/[LCM of 120,2994]= 31/59880
Therefore, the GCF of 7533/120,4712/2994 is 31/59880.
To find the highest common factor of 7533,4712, we have to find the factors of both numbers and list the highest common factor.
The factors of 7533 are 1, 3, 9, 27, 31, 81, 93, 243, 279, 837, 2511, 7533
The factors of 4712 are 1, 2, 4, 8, 19, 31, 38, 62, 76, 124, 152, 248, 589, 1178, 2356, 4712
The HCF of 7533,4712 is 31.
Lets's calculate GCF of 7533,4712
| 31 | 7533, 4712 |
| 243, 152 |
∴ So the GCF of the given numbers is 31 = 31
Greatest Common Factor of 7533,4712 By Matching Biggest Common Factor Method
Now, list down the factors of 7533
:1,3,9,27,31,81,93,243,279,837,2511,7533
Now, list down the factors of 4712
:1,2,4,8,19,31,38,62,76,124,152,248,589,1178,2356,4712
Greatest Common Factor
We found the factors 7533,4712 . The biggest common factor number is the GCF number.
So the greatest common factor 7533,4712 is 31.
Lets's calculate LCM of 120,2994
| 2 | 120, 2994 |
| 3 | 60, 1497 |
| 20, 499 |
∴ So the LCM of the given numbers is 2 x 3 x 20 x 499 = 59880
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/59880
Therefore, the GCF of Fractions 7533/120,4712/2994 is 31/59880
Least Common Multiple of 120,2994 with GCF Formula
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 120,2994 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(120,2994) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(120,2994) x common factors =6 x 1 = 6
LCM(120,2994) = ( 120 × 2994 ) / 6
LCM(120,2994) = 359280 / 6
LCM(120,2994) = 59880
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FAQs on GCF of Fractions of 7533/120, 4712/2994
1. What is the HCF of 7533,4712?
The HCF of 7533,4712 is 31
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 7533/120, 4712/2994?
Answer: GCF of Numerators as per given numbers 7533/120, 4712/2994 is
GCF of Numerators i.e. for 7533,4712 is 31
LCM of denominators i.e. for 120,2994 is 59880.
Thus, GCF of Fractions is 31/59880.Finally, GCF of Fractions for 7533/120, 4712/2994 is 31/59880.