GCF of 5684/822, 1302/5322
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5684/822, 1302/5322 i.e 14/729114 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5684/822, 1302/5322.
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 5684/822,1302/5322?
Given fractions are 5684/822,1302/5322
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 5684/822,1302/5322, numerators are 5684,1302
Denominators are 822,5322
The GCF of 5684,1302 is 14 .
LCM of 822,5322 is 729114.
The greatest common factor of 5684/822,1302/5322 = [GCF of 5684,1302]/[LCM of 822,5322]= 14/729114
Therefore, the GCF of 5684/822,1302/5322 is 14/729114.
To find the highest common factor of 5684,1302, we have to find the factors of both numbers and list the highest common factor.
The factors of 5684 are 1, 2, 4, 7, 14, 28, 29, 49, 58, 98, 116, 196, 203, 406, 812, 1421, 2842, 5684
The factors of 1302 are 1, 2, 3, 6, 7, 14, 21, 31, 42, 62, 93, 186, 217, 434, 651, 1302
The HCF of 5684,1302 is 14.
Lets's calculate GCF of 5684,1302
| 2 | 5684, 1302 |
| 7 | 2842, 651 |
| 406, 93 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 5684,1302 By Matching Biggest Common Factor Method
Now, list down the factors of 5684
:1,2,4,7,14,28,29,49,58,98,116,196,203,406,812,1421,2842,5684
Now, list down the factors of 1302
:1,2,3,6,7,14,21,31,42,62,93,186,217,434,651,1302
Greatest Common Factor
We found the factors 5684,1302 . The biggest common factor number is the GCF number.
So the greatest common factor 5684,1302 is 14.
Lets's calculate LCM of 822,5322
| 2 | 822, 5322 |
| 3 | 411, 2661 |
| 137, 887 |
∴ So the LCM of the given numbers is 2 x 3 x 137 x 887 = 729114
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/729114
Therefore, the GCF of Fractions 5684/822,1302/5322 is 14/729114
Least Common Multiple of 822,5322 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 822,5322 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(822,5322) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(822,5322) x common factors =6 x 1 = 6
LCM(822,5322) = ( 822 × 5322 ) / 6
LCM(822,5322) = 4374684 / 6
LCM(822,5322) = 729114
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FAQs on GCF of Fractions of 5684/822, 1302/5322
1. What is the HCF of 5684,1302?
The HCF of 5684,1302 is 14
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 5684/822, 1302/5322?
Answer: GCF of Numerators as per given numbers 5684/822, 1302/5322 is
GCF of Numerators i.e. for 5684,1302 is 14
LCM of denominators i.e. for 822,5322 is 729114.
Thus, GCF of Fractions is 14/729114.Finally, GCF of Fractions for 5684/822, 1302/5322 is 14/729114.