GCF of 7524/52, 1728/611
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7524/52, 1728/611 i.e 36/2444 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7524/52, 1728/611.
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 7524/52,1728/611?
Given fractions are 7524/52,1728/611
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 7524/52,1728/611, numerators are 7524,1728
Denominators are 52,611
The GCF of 7524,1728 is 36 .
LCM of 52,611 is 2444.
The greatest common factor of 7524/52,1728/611 = [GCF of 7524,1728]/[LCM of 52,611]= 36/2444
Therefore, the GCF of 7524/52,1728/611 is 36/2444.
To find the highest common factor of 7524,1728, we have to find the factors of both numbers and list the highest common factor.
The factors of 7524 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 19, 22, 33, 36, 38, 44, 57, 66, 76, 99, 114, 132, 171, 198, 209, 228, 342, 396, 418, 627, 684, 836, 1254, 1881, 2508, 3762, 7524
The factors of 1728 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728
The HCF of 7524,1728 is 36.
Lets's calculate GCF of 7524,1728
| 2 | 7524, 1728 |
| 2 | 3762, 864 |
| 3 | 1881, 432 |
| 3 | 627, 144 |
| 209, 48 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 3 = 36
Greatest Common Factor of 7524,1728 By Matching Biggest Common Factor Method
Now, list down the factors of 7524
:1,2,3,4,6,9,11,12,18,19,22,33,36,38,44,57,66,76,99,114,132,171,198,209,228,342,396,418,627,684,836,1254,1881,2508,3762,7524
Now, list down the factors of 1728
:1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,64,72,96,108,144,192,216,288,432,576,864,1728
Greatest Common Factor
We found the factors 7524,1728 . The biggest common factor number is the GCF number.
So the greatest common factor 7524,1728 is 36.
Lets's calculate LCM of 52,611
| 13 | 52, 611 |
| 4, 47 |
∴ So the LCM of the given numbers is 13 x 4 x 47 = 2444
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 36/2444
Therefore, the GCF of Fractions 7524/52,1728/611 is 36/2444
Least Common Multiple of 52,611 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 52,611 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(52,611) = 13
common factors(in case of two or more numbers have common factors) = 1
GCF(52,611) x common factors =13 x 1 = 13
LCM(52,611) = ( 52 × 611 ) / 13
LCM(52,611) = 31772 / 13
LCM(52,611) = 2444
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 7524/52, 1728/611
1. What is the HCF of 7524,1728?
The HCF of 7524,1728 is 36
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 7524/52, 1728/611?
Answer: GCF of Numerators as per given numbers 7524/52, 1728/611 is
GCF of Numerators i.e. for 7524,1728 is 36
LCM of denominators i.e. for 52,611 is 2444.
Thus, GCF of Fractions is 36/2444.Finally, GCF of Fractions for 7524/52, 1728/611 is 36/2444.