GCF of 5214/975, 6720/2120
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5214/975, 6720/2120 i.e 6/413400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5214/975, 6720/2120.
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 5214/975,6720/2120?
Given fractions are 5214/975,6720/2120
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 5214/975,6720/2120, numerators are 5214,6720
Denominators are 975,2120
The GCF of 5214,6720 is 6 .
LCM of 975,2120 is 413400.
The greatest common factor of 5214/975,6720/2120 = [GCF of 5214,6720]/[LCM of 975,2120]= 6/413400
Therefore, the GCF of 5214/975,6720/2120 is 6/413400.
To find the highest common factor of 5214,6720, we have to find the factors of both numbers and list the highest common factor.
The factors of 5214 are 1, 2, 3, 6, 11, 22, 33, 66, 79, 158, 237, 474, 869, 1738, 2607, 5214
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 HCF of 5214,6720 is 6.
Lets's calculate GCF of 5214,6720
| 2 | 5214, 6720 |
| 3 | 2607, 3360 |
| 869, 1120 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 5214,6720 By Matching Biggest Common Factor Method
Now, list down the factors of 5214
:1,2,3,6,11,22,33,66,79,158,237,474,869,1738,2607,5214
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
Greatest Common Factor
We found the factors 5214,6720 . The biggest common factor number is the GCF number.
So the greatest common factor 5214,6720 is 6.
Lets's calculate LCM of 975,2120
| 5 | 975, 2120 |
| 195, 424 |
∴ So the LCM of the given numbers is 5 x 195 x 424 = 413400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/413400
Therefore, the GCF of Fractions 5214/975,6720/2120 is 6/413400
Least Common Multiple of 975,2120 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 975,2120 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(975,2120) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(975,2120) x common factors =5 x 1 = 5
LCM(975,2120) = ( 975 × 2120 ) / 5
LCM(975,2120) = 2067000 / 5
LCM(975,2120) = 413400
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FAQs on GCF of Fractions of 5214/975, 6720/2120
1. What is the HCF of 5214,6720?
The HCF of 5214,6720 is 6
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 5214/975, 6720/2120?
Answer: GCF of Numerators as per given numbers 5214/975, 6720/2120 is
GCF of Numerators i.e. for 5214,6720 is 6
LCM of denominators i.e. for 975,2120 is 413400.
Thus, GCF of Fractions is 6/413400.Finally, GCF of Fractions for 5214/975, 6720/2120 is 6/413400.