GCF of 7189/516, 1140/3200
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7189/516, 1140/3200 i.e 1/412800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7189/516, 1140/3200.
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 7189/516,1140/3200?
Given fractions are 7189/516,1140/3200
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 7189/516,1140/3200, numerators are 7189,1140
Denominators are 516,3200
The GCF of 7189,1140 is 1 .
LCM of 516,3200 is 412800.
The greatest common factor of 7189/516,1140/3200 = [GCF of 7189,1140]/[LCM of 516,3200]= 1/412800
Therefore, the GCF of 7189/516,1140/3200 is 1/412800.
To find the highest common factor of 7189,1140, we have to find the factors of both numbers and list the highest common factor.
The factors of 7189 are 1, 7, 13, 79, 91, 553, 1027, 7189
The factors of 1140 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 19, 20, 30, 38, 57, 60, 76, 95, 114, 190, 228, 285, 380, 570, 1140
The HCF of 7189,1140 is 1.
Lets's calculate GCF of 7189,1140
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 7189,1140 By Matching Biggest Common Factor Method
Now, list down the factors of 7189
:1,7,13,79,91,553,1027,7189
Now, list down the factors of 1140
:1,2,3,4,5,6,10,12,15,19,20,30,38,57,60,76,95,114,190,228,285,380,570,1140
Greatest Common Factor
We found the factors 7189,1140 . The biggest common factor number is the GCF number.
So the greatest common factor 7189,1140 is 1.
Lets's calculate LCM of 516,3200
| 2 | 516, 3200 |
| 2 | 258, 1600 |
| 129, 800 |
∴ So the LCM of the given numbers is 2 x 2 x 129 x 800 = 412800
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/412800
Therefore, the GCF of Fractions 7189/516,1140/3200 is 1/412800
Least Common Multiple of 516,3200 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 516,3200 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(516,3200) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(516,3200) x common factors =4 x 1 = 4
LCM(516,3200) = ( 516 × 3200 ) / 4
LCM(516,3200) = 1651200 / 4
LCM(516,3200) = 412800
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FAQs on GCF of Fractions of 7189/516, 1140/3200
1. What is the HCF of 7189,1140?
The HCF of 7189,1140 is 1
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 7189/516, 1140/3200?
Answer: GCF of Numerators as per given numbers 7189/516, 1140/3200 is
GCF of Numerators i.e. for 7189,1140 is 1
LCM of denominators i.e. for 516,3200 is 412800.
Thus, GCF of Fractions is 1/412800.Finally, GCF of Fractions for 7189/516, 1140/3200 is 1/412800.