GCF of 260/310, 312/812
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 260/310, 312/812 i.e 52/125860 easily. The following is the detailed procedure to determine the greatest common factor of fractions 260/310, 312/812.
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 260/310,312/812?
Given fractions are 260/310,312/812
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 260/310,312/812, numerators are 260,312
Denominators are 310,812
The GCF of 260,312 is 52 .
LCM of 310,812 is 125860.
The greatest common factor of 260/310,312/812 = [GCF of 260,312]/[LCM of 310,812]= 52/125860
Therefore, the GCF of 260/310,312/812 is 52/125860.
To find the highest common factor of 260,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 260 are 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 260,312 is 52.
Lets's calculate GCF of 260,312
| 2 | 260, 312 |
| 2 | 130, 156 |
| 13 | 65, 78 |
| 5, 6 |
∴ So the GCF of the given numbers is 2 x 2 x 13 = 52
Greatest Common Factor of 260,312 By Matching Biggest Common Factor Method
Now, list down the factors of 260
:1,2,4,5,10,13,20,26,52,65,130,260
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 260,312 . The biggest common factor number is the GCF number.
So the greatest common factor 260,312 is 52.
Lets's calculate LCM of 310,812
| 2 | 310, 812 |
| 155, 406 |
∴ So the LCM of the given numbers is 2 x 155 x 406 = 125860
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 52/125860
Therefore, the GCF of Fractions 260/310,312/812 is 52/125860
Least Common Multiple of 310,812 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 310,812 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(310,812) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(310,812) x common factors =2 x 1 = 2
LCM(310,812) = ( 310 × 812 ) / 2
LCM(310,812) = 251720 / 2
LCM(310,812) = 125860
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FAQs on GCF of Fractions of 260/310, 312/812
1. What is the HCF of 260,312?
The HCF of 260,312 is 52
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 260/310, 312/812?
Answer: GCF of Numerators as per given numbers 260/310, 312/812 is
GCF of Numerators i.e. for 260,312 is 52
LCM of denominators i.e. for 310,812 is 125860.
Thus, GCF of Fractions is 52/125860.Finally, GCF of Fractions for 260/310, 312/812 is 52/125860.