GCF of 7548/912, 7380/9984
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7548/912, 7380/9984 i.e 12/189696 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7548/912, 7380/9984.
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 7548/912,7380/9984?
Given fractions are 7548/912,7380/9984
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 7548/912,7380/9984, numerators are 7548,7380
Denominators are 912,9984
The GCF of 7548,7380 is 12 .
LCM of 912,9984 is 189696.
The greatest common factor of 7548/912,7380/9984 = [GCF of 7548,7380]/[LCM of 912,9984]= 12/189696
Therefore, the GCF of 7548/912,7380/9984 is 12/189696.
To find the highest common factor of 7548,7380, we have to find the factors of both numbers and list the highest common factor.
The factors of 7548 are 1, 2, 3, 4, 6, 12, 17, 34, 37, 51, 68, 74, 102, 111, 148, 204, 222, 444, 629, 1258, 1887, 2516, 3774, 7548
The factors of 7380 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 41, 45, 60, 82, 90, 123, 164, 180, 205, 246, 369, 410, 492, 615, 738, 820, 1230, 1476, 1845, 2460, 3690, 7380
The HCF of 7548,7380 is 12.
Lets's calculate GCF of 7548,7380
| 2 | 7548, 7380 |
| 2 | 3774, 3690 |
| 3 | 1887, 1845 |
| 629, 615 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 7548,7380 By Matching Biggest Common Factor Method
Now, list down the factors of 7548
:1,2,3,4,6,12,17,34,37,51,68,74,102,111,148,204,222,444,629,1258,1887,2516,3774,7548
Now, list down the factors of 7380
:1,2,3,4,5,6,9,10,12,15,18,20,30,36,41,45,60,82,90,123,164,180,205,246,369,410,492,615,738,820,1230,1476,1845,2460,3690,7380
Greatest Common Factor
We found the factors 7548,7380 . The biggest common factor number is the GCF number.
So the greatest common factor 7548,7380 is 12.
Lets's calculate LCM of 912,9984
| 2 | 912, 9984 |
| 2 | 456, 4992 |
| 2 | 228, 2496 |
| 2 | 114, 1248 |
| 3 | 57, 624 |
| 19, 208 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 3 x 19 x 208 = 189696
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/189696
Therefore, the GCF of Fractions 7548/912,7380/9984 is 12/189696
Least Common Multiple of 912,9984 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 912,9984 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(912,9984) = 48
common factors(in case of two or more numbers have common factors) = 1
GCF(912,9984) x common factors =48 x 1 = 48
LCM(912,9984) = ( 912 × 9984 ) / 48
LCM(912,9984) = 9105408 / 48
LCM(912,9984) = 189696
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FAQs on GCF of Fractions of 7548/912, 7380/9984
1. What is the HCF of 7548,7380?
The HCF of 7548,7380 is 12
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 7548/912, 7380/9984?
Answer: GCF of Numerators as per given numbers 7548/912, 7380/9984 is
GCF of Numerators i.e. for 7548,7380 is 12
LCM of denominators i.e. for 912,9984 is 189696.
Thus, GCF of Fractions is 12/189696.Finally, GCF of Fractions for 7548/912, 7380/9984 is 12/189696.