GCF of 4125/724, 7722/9288
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4125/724, 7722/9288 i.e 33/1681128 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4125/724, 7722/9288.
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 4125/724,7722/9288?
Given fractions are 4125/724,7722/9288
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 4125/724,7722/9288, numerators are 4125,7722
Denominators are 724,9288
The GCF of 4125,7722 is 33 .
LCM of 724,9288 is 1681128.
The greatest common factor of 4125/724,7722/9288 = [GCF of 4125,7722]/[LCM of 724,9288]= 33/1681128
Therefore, the GCF of 4125/724,7722/9288 is 33/1681128.
To find the highest common factor of 4125,7722, we have to find the factors of both numbers and list the highest common factor.
The factors of 4125 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 125, 165, 275, 375, 825, 1375, 4125
The factors of 7722 are 1, 2, 3, 6, 9, 11, 13, 18, 22, 26, 27, 33, 39, 54, 66, 78, 99, 117, 143, 198, 234, 286, 297, 351, 429, 594, 702, 858, 1287, 2574, 3861, 7722
The HCF of 4125,7722 is 33.
Lets's calculate GCF of 4125,7722
| 3 | 4125, 7722 |
| 11 | 1375, 2574 |
| 125, 234 |
∴ So the GCF of the given numbers is 3 x 11 = 33
Greatest Common Factor of 4125,7722 By Matching Biggest Common Factor Method
Now, list down the factors of 4125
:1,3,5,11,15,25,33,55,75,125,165,275,375,825,1375,4125
Now, list down the factors of 7722
:1,2,3,6,9,11,13,18,22,26,27,33,39,54,66,78,99,117,143,198,234,286,297,351,429,594,702,858,1287,2574,3861,7722
Greatest Common Factor
We found the factors 4125,7722 . The biggest common factor number is the GCF number.
So the greatest common factor 4125,7722 is 33.
Lets's calculate LCM of 724,9288
| 2 | 724, 9288 |
| 2 | 362, 4644 |
| 181, 2322 |
∴ So the LCM of the given numbers is 2 x 2 x 181 x 2322 = 1681128
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 33/1681128
Therefore, the GCF of Fractions 4125/724,7722/9288 is 33/1681128
Least Common Multiple of 724,9288 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 724,9288 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(724,9288) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(724,9288) x common factors =4 x 1 = 4
LCM(724,9288) = ( 724 × 9288 ) / 4
LCM(724,9288) = 6724512 / 4
LCM(724,9288) = 1681128
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FAQs on GCF of Fractions of 4125/724, 7722/9288
1. What is the HCF of 4125,7722?
The HCF of 4125,7722 is 33
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 4125/724, 7722/9288?
Answer: GCF of Numerators as per given numbers 4125/724, 7722/9288 is
GCF of Numerators i.e. for 4125,7722 is 33
LCM of denominators i.e. for 724,9288 is 1681128.
Thus, GCF of Fractions is 33/1681128.Finally, GCF of Fractions for 4125/724, 7722/9288 is 33/1681128.