GCF of 5302/812, 1400/6708
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5302/812, 1400/6708 i.e 2/1361724 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5302/812, 1400/6708.
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 5302/812,1400/6708?
Given fractions are 5302/812,1400/6708
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 5302/812,1400/6708, numerators are 5302,1400
Denominators are 812,6708
The GCF of 5302,1400 is 2 .
LCM of 812,6708 is 1361724.
The greatest common factor of 5302/812,1400/6708 = [GCF of 5302,1400]/[LCM of 812,6708]= 2/1361724
Therefore, the GCF of 5302/812,1400/6708 is 2/1361724.
To find the highest common factor of 5302,1400, we have to find the factors of both numbers and list the highest common factor.
The factors of 5302 are 1, 2, 11, 22, 241, 482, 2651, 5302
The factors of 1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400
The HCF of 5302,1400 is 2.
Lets's calculate GCF of 5302,1400
| 2 | 5302, 1400 |
| 2651, 700 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 5302,1400 By Matching Biggest Common Factor Method
Now, list down the factors of 5302
:1,2,11,22,241,482,2651,5302
Now, list down the factors of 1400
:1,2,4,5,7,8,10,14,20,25,28,35,40,50,56,70,100,140,175,200,280,350,700,1400
Greatest Common Factor
We found the factors 5302,1400 . The biggest common factor number is the GCF number.
So the greatest common factor 5302,1400 is 2.
Lets's calculate LCM of 812,6708
| 2 | 812, 6708 |
| 2 | 406, 3354 |
| 203, 1677 |
∴ So the LCM of the given numbers is 2 x 2 x 203 x 1677 = 1361724
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1361724
Therefore, the GCF of Fractions 5302/812,1400/6708 is 2/1361724
Least Common Multiple of 812,6708 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 812,6708 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(812,6708) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(812,6708) x common factors =4 x 1 = 4
LCM(812,6708) = ( 812 × 6708 ) / 4
LCM(812,6708) = 5446896 / 4
LCM(812,6708) = 1361724
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FAQs on GCF of Fractions of 5302/812, 1400/6708
1. What is the HCF of 5302,1400?
The HCF of 5302,1400 is 2
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 5302/812, 1400/6708?
Answer: GCF of Numerators as per given numbers 5302/812, 1400/6708 is
GCF of Numerators i.e. for 5302,1400 is 2
LCM of denominators i.e. for 812,6708 is 1361724.
Thus, GCF of Fractions is 2/1361724.Finally, GCF of Fractions for 5302/812, 1400/6708 is 2/1361724.