GCF of 3542/459, 5720/8313
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3542/459, 5720/8313 i.e 22/74817 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3542/459, 5720/8313.
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 3542/459,5720/8313?
Given fractions are 3542/459,5720/8313
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 3542/459,5720/8313, numerators are 3542,5720
Denominators are 459,8313
The GCF of 3542,5720 is 22 .
LCM of 459,8313 is 74817.
The greatest common factor of 3542/459,5720/8313 = [GCF of 3542,5720]/[LCM of 459,8313]= 22/74817
Therefore, the GCF of 3542/459,5720/8313 is 22/74817.
To find the highest common factor of 3542,5720, we have to find the factors of both numbers and list the highest common factor.
The factors of 3542 are 1, 2, 7, 11, 14, 22, 23, 46, 77, 154, 161, 253, 322, 506, 1771, 3542
The factors of 5720 are 1, 2, 4, 5, 8, 10, 11, 13, 20, 22, 26, 40, 44, 52, 55, 65, 88, 104, 110, 130, 143, 220, 260, 286, 440, 520, 572, 715, 1144, 1430, 2860, 5720
The HCF of 3542,5720 is 22.
Lets's calculate GCF of 3542,5720
| 2 | 3542, 5720 |
| 11 | 1771, 2860 |
| 161, 260 |
∴ So the GCF of the given numbers is 2 x 11 = 22
Greatest Common Factor of 3542,5720 By Matching Biggest Common Factor Method
Now, list down the factors of 3542
:1,2,7,11,14,22,23,46,77,154,161,253,322,506,1771,3542
Now, list down the factors of 5720
:1,2,4,5,8,10,11,13,20,22,26,40,44,52,55,65,88,104,110,130,143,220,260,286,440,520,572,715,1144,1430,2860,5720
Greatest Common Factor
We found the factors 3542,5720 . The biggest common factor number is the GCF number.
So the greatest common factor 3542,5720 is 22.
Lets's calculate LCM of 459,8313
| 3 | 459, 8313 |
| 17 | 153, 2771 |
| 9, 163 |
∴ So the LCM of the given numbers is 3 x 17 x 9 x 163 = 74817
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/74817
Therefore, the GCF of Fractions 3542/459,5720/8313 is 22/74817
Least Common Multiple of 459,8313 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 459,8313 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(459,8313) = 51
common factors(in case of two or more numbers have common factors) = 1
GCF(459,8313) x common factors =51 x 1 = 51
LCM(459,8313) = ( 459 × 8313 ) / 51
LCM(459,8313) = 3815667 / 51
LCM(459,8313) = 74817
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FAQs on GCF of Fractions of 3542/459, 5720/8313
1. What is the HCF of 3542,5720?
The HCF of 3542,5720 is 22
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 3542/459, 5720/8313?
Answer: GCF of Numerators as per given numbers 3542/459, 5720/8313 is
GCF of Numerators i.e. for 3542,5720 is 22
LCM of denominators i.e. for 459,8313 is 74817.
Thus, GCF of Fractions is 22/74817.Finally, GCF of Fractions for 3542/459, 5720/8313 is 22/74817.