GCF of 869/12, 902/678
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 869/12, 902/678 i.e 11/1356 easily. The following is the detailed procedure to determine the greatest common factor of fractions 869/12, 902/678.
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 869/12,902/678?
Given fractions are 869/12,902/678
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 869/12,902/678, numerators are 869,902
Denominators are 12,678
The GCF of 869,902 is 11 .
LCM of 12,678 is 1356.
The greatest common factor of 869/12,902/678 = [GCF of 869,902]/[LCM of 12,678]= 11/1356
Therefore, the GCF of 869/12,902/678 is 11/1356.
To find the highest common factor of 869,902, we have to find the factors of both numbers and list the highest common factor.
The factors of 869 are 1, 11, 79, 869
The factors of 902 are 1, 2, 11, 22, 41, 82, 451, 902
The HCF of 869,902 is 11.
Lets's calculate GCF of 869,902
| 11 | 869, 902 |
| 79, 82 |
∴ So the GCF of the given numbers is 11 = 11
Greatest Common Factor of 869,902 By Matching Biggest Common Factor Method
Now, list down the factors of 869
:1,11,79,869
Now, list down the factors of 902
:1,2,11,22,41,82,451,902
Greatest Common Factor
We found the factors 869,902 . The biggest common factor number is the GCF number.
So the greatest common factor 869,902 is 11.
Lets's calculate LCM of 12,678
| 2 | 12, 678 |
| 3 | 6, 339 |
| 2, 113 |
∴ So the LCM of the given numbers is 2 x 3 x 2 x 113 = 1356
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/1356
Therefore, the GCF of Fractions 869/12,902/678 is 11/1356
Least Common Multiple of 12,678 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 12,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,678) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(12,678) x common factors =6 x 1 = 6
LCM(12,678) = ( 12 × 678 ) / 6
LCM(12,678) = 8136 / 6
LCM(12,678) = 1356
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FAQs on GCF of Fractions of 869/12, 902/678
1. What is the HCF of 869,902?
The HCF of 869,902 is 11
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 869/12, 902/678?
Answer: GCF of Numerators as per given numbers 869/12, 902/678 is
GCF of Numerators i.e. for 869,902 is 11
LCM of denominators i.e. for 12,678 is 1356.
Thus, GCF of Fractions is 11/1356.Finally, GCF of Fractions for 869/12, 902/678 is 11/1356.