GCF of 753/512, 6624/2944
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 753/512, 6624/2944 i.e 3/11776 easily. The following is the detailed procedure to determine the greatest common factor of fractions 753/512, 6624/2944.
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 753/512,6624/2944?
Given fractions are 753/512,6624/2944
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 753/512,6624/2944, numerators are 753,6624
Denominators are 512,2944
The GCF of 753,6624 is 3 .
LCM of 512,2944 is 11776.
The greatest common factor of 753/512,6624/2944 = [GCF of 753,6624]/[LCM of 512,2944]= 3/11776
Therefore, the GCF of 753/512,6624/2944 is 3/11776.
To find the highest common factor of 753,6624, we have to find the factors of both numbers and list the highest common factor.
The factors of 753 are 1, 3, 251, 753
The factors of 6624 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 23, 24, 32, 36, 46, 48, 69, 72, 92, 96, 138, 144, 184, 207, 276, 288, 368, 414, 552, 736, 828, 1104, 1656, 2208, 3312, 6624
The HCF of 753,6624 is 3.
Lets's calculate GCF of 753,6624
| 3 | 753, 6624 |
| 251, 2208 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 753,6624 By Matching Biggest Common Factor Method
Now, list down the factors of 753
:1,3,251,753
Now, list down the factors of 6624
:1,2,3,4,6,8,9,12,16,18,23,24,32,36,46,48,69,72,92,96,138,144,184,207,276,288,368,414,552,736,828,1104,1656,2208,3312,6624
Greatest Common Factor
We found the factors 753,6624 . The biggest common factor number is the GCF number.
So the greatest common factor 753,6624 is 3.
Lets's calculate LCM of 512,2944
| 2 | 512, 2944 |
| 2 | 256, 1472 |
| 2 | 128, 736 |
| 2 | 64, 368 |
| 2 | 32, 184 |
| 2 | 16, 92 |
| 2 | 8, 46 |
| 4, 23 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 4 x 23 = 11776
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/11776
Therefore, the GCF of Fractions 753/512,6624/2944 is 3/11776
Least Common Multiple of 512,2944 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 512,2944 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(512,2944) = 128
common factors(in case of two or more numbers have common factors) = 1
GCF(512,2944) x common factors =128 x 1 = 128
LCM(512,2944) = ( 512 × 2944 ) / 128
LCM(512,2944) = 1507328 / 128
LCM(512,2944) = 11776
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FAQs on GCF of Fractions of 753/512, 6624/2944
1. What is the HCF of 753,6624?
The HCF of 753,6624 is 3
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 753/512, 6624/2944?
Answer: GCF of Numerators as per given numbers 753/512, 6624/2944 is
GCF of Numerators i.e. for 753,6624 is 3
LCM of denominators i.e. for 512,2944 is 11776.
Thus, GCF of Fractions is 3/11776.Finally, GCF of Fractions for 753/512, 6624/2944 is 3/11776.