GCF of 6720/469, 5688/5172
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6720/469, 5688/5172 i.e 24/2425668 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6720/469, 5688/5172.
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 6720/469,5688/5172?
Given fractions are 6720/469,5688/5172
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 6720/469,5688/5172, numerators are 6720,5688
Denominators are 469,5172
The GCF of 6720,5688 is 24 .
LCM of 469,5172 is 2425668.
The greatest common factor of 6720/469,5688/5172 = [GCF of 6720,5688]/[LCM of 469,5172]= 24/2425668
Therefore, the GCF of 6720/469,5688/5172 is 24/2425668.
To find the highest common factor of 6720,5688, we have to find the factors of both numbers and list the highest common factor.
The factors of 6720 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 56, 60, 64, 70, 80, 84, 96, 105, 112, 120, 140, 160, 168, 192, 210, 224, 240, 280, 320, 336, 420, 448, 480, 560, 672, 840, 960, 1120, 1344, 1680, 2240, 3360, 6720
The factors of 5688 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 79, 158, 237, 316, 474, 632, 711, 948, 1422, 1896, 2844, 5688
The HCF of 6720,5688 is 24.
Lets's calculate GCF of 6720,5688
| 2 | 6720, 5688 |
| 2 | 3360, 2844 |
| 2 | 1680, 1422 |
| 3 | 840, 711 |
| 280, 237 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24
Greatest Common Factor of 6720,5688 By Matching Biggest Common Factor Method
Now, list down the factors of 6720
:1,2,3,4,5,6,7,8,10,12,14,15,16,20,21,24,28,30,32,35,40,42,48,56,60,64,70,80,84,96,105,112,120,140,160,168,192,210,224,240,280,320,336,420,448,480,560,672,840,960,1120,1344,1680,2240,3360,6720
Now, list down the factors of 5688
:1,2,3,4,6,8,9,12,18,24,36,72,79,158,237,316,474,632,711,948,1422,1896,2844,5688
Greatest Common Factor
We found the factors 6720,5688 . The biggest common factor number is the GCF number.
So the greatest common factor 6720,5688 is 24.
Lets's calculate LCM of 469,5172
Given numbers has no common factors except 1. So, there LCM is their product i.e 2425668
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/2425668
Therefore, the GCF of Fractions 6720/469,5688/5172 is 24/2425668
Least Common Multiple of 469,5172 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 469,5172 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(469,5172) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(469,5172) x common factors =1 x 1 = 1
LCM(469,5172) = ( 469 × 5172 ) / 1
LCM(469,5172) = 2425668 / 1
LCM(469,5172) = 2425668
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FAQs on GCF of Fractions of 6720/469, 5688/5172
1. What is the HCF of 6720,5688?
The HCF of 6720,5688 is 24
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 6720/469, 5688/5172?
Answer: GCF of Numerators as per given numbers 6720/469, 5688/5172 is
GCF of Numerators i.e. for 6720,5688 is 24
LCM of denominators i.e. for 469,5172 is 2425668.
Thus, GCF of Fractions is 24/2425668.Finally, GCF of Fractions for 6720/469, 5688/5172 is 24/2425668.