GCF of 7056/564, 6912/269
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7056/564, 6912/269 i.e 144/151716 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7056/564, 6912/269.
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 7056/564,6912/269?
Given fractions are 7056/564,6912/269
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 7056/564,6912/269, numerators are 7056,6912
Denominators are 564,269
The GCF of 7056,6912 is 144 .
LCM of 564,269 is 151716.
The greatest common factor of 7056/564,6912/269 = [GCF of 7056,6912]/[LCM of 564,269]= 144/151716
Therefore, the GCF of 7056/564,6912/269 is 144/151716.
To find the highest common factor of 7056,6912, we have to find the factors of both numbers and list the highest common factor.
The factors of 7056 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 49, 56, 63, 72, 84, 98, 112, 126, 144, 147, 168, 196, 252, 294, 336, 392, 441, 504, 588, 784, 882, 1008, 1176, 1764, 2352, 3528, 7056
The factors of 6912 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 576, 768, 864, 1152, 1728, 2304, 3456, 6912
The HCF of 7056,6912 is 144.
Lets's calculate GCF of 7056,6912
| 2 | 7056, 6912 |
| 2 | 3528, 3456 |
| 2 | 1764, 1728 |
| 2 | 882, 864 |
| 3 | 441, 432 |
| 3 | 147, 144 |
| 49, 48 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 3 x 3 = 144
Greatest Common Factor of 7056,6912 By Matching Biggest Common Factor Method
Now, list down the factors of 7056
:1,2,3,4,6,7,8,9,12,14,16,18,21,24,28,36,42,48,49,56,63,72,84,98,112,126,144,147,168,196,252,294,336,392,441,504,588,784,882,1008,1176,1764,2352,3528,7056
Now, list down the factors of 6912
:1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,64,72,96,108,128,144,192,216,256,288,384,432,576,768,864,1152,1728,2304,3456,6912
Greatest Common Factor
We found the factors 7056,6912 . The biggest common factor number is the GCF number.
So the greatest common factor 7056,6912 is 144.
Lets's calculate LCM of 564,269
Given numbers has no common factors except 1. So, there LCM is their product i.e 151716
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 144/151716
Therefore, the GCF of Fractions 7056/564,6912/269 is 144/151716
Least Common Multiple of 564,269 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 564,269 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(564,269) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(564,269) x common factors =1 x 1 = 1
LCM(564,269) = ( 564 × 269 ) / 1
LCM(564,269) = 151716 / 1
LCM(564,269) = 151716
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FAQs on GCF of Fractions of 7056/564, 6912/269
1. What is the HCF of 7056,6912?
The HCF of 7056,6912 is 144
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 7056/564, 6912/269?
Answer: GCF of Numerators as per given numbers 7056/564, 6912/269 is
GCF of Numerators i.e. for 7056,6912 is 144
LCM of denominators i.e. for 564,269 is 151716.
Thus, GCF of Fractions is 144/151716.Finally, GCF of Fractions for 7056/564, 6912/269 is 144/151716.