GCF of 909/812, 5382/348
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 909/812, 5382/348 i.e 9/2436 easily. The following is the detailed procedure to determine the greatest common factor of fractions 909/812, 5382/348.
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 909/812,5382/348?
Given fractions are 909/812,5382/348
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 909/812,5382/348, numerators are 909,5382
Denominators are 812,348
The GCF of 909,5382 is 9 .
LCM of 812,348 is 2436.
The greatest common factor of 909/812,5382/348 = [GCF of 909,5382]/[LCM of 812,348]= 9/2436
Therefore, the GCF of 909/812,5382/348 is 9/2436.
To find the highest common factor of 909,5382, we have to find the factors of both numbers and list the highest common factor.
The factors of 909 are 1, 3, 9, 101, 303, 909
The factors of 5382 are 1, 2, 3, 6, 9, 13, 18, 23, 26, 39, 46, 69, 78, 117, 138, 207, 234, 299, 414, 598, 897, 1794, 2691, 5382
The HCF of 909,5382 is 9.
Lets's calculate GCF of 909,5382
| 3 | 909, 5382 |
| 3 | 303, 1794 |
| 101, 598 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 909,5382 By Matching Biggest Common Factor Method
Now, list down the factors of 909
:1,3,9,101,303,909
Now, list down the factors of 5382
:1,2,3,6,9,13,18,23,26,39,46,69,78,117,138,207,234,299,414,598,897,1794,2691,5382
Greatest Common Factor
We found the factors 909,5382 . The biggest common factor number is the GCF number.
So the greatest common factor 909,5382 is 9.
Lets's calculate LCM of 812,348
| 2 | 812, 348 |
| 2 | 406, 174 |
| 29 | 203, 87 |
| 7, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 29 x 7 x 3 = 2436
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/2436
Therefore, the GCF of Fractions 909/812,5382/348 is 9/2436
Least Common Multiple of 812,348 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 812,348 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(812,348) = 116
common factors(in case of two or more numbers have common factors) = 1
GCF(812,348) x common factors =116 x 1 = 116
LCM(812,348) = ( 812 × 348 ) / 116
LCM(812,348) = 282576 / 116
LCM(812,348) = 2436
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FAQs on GCF of Fractions of 909/812, 5382/348
1. What is the HCF of 909,5382?
The HCF of 909,5382 is 9
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 909/812, 5382/348?
Answer: GCF of Numerators as per given numbers 909/812, 5382/348 is
GCF of Numerators i.e. for 909,5382 is 9
LCM of denominators i.e. for 812,348 is 2436.
Thus, GCF of Fractions is 9/2436.Finally, GCF of Fractions for 909/812, 5382/348 is 9/2436.