GCF of 906/390, 5340/120
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 906/390, 5340/120 i.e 6/1560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 906/390, 5340/120.
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 906/390,5340/120?
Given fractions are 906/390,5340/120
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 906/390,5340/120, numerators are 906,5340
Denominators are 390,120
The GCF of 906,5340 is 6 .
LCM of 390,120 is 1560.
The greatest common factor of 906/390,5340/120 = [GCF of 906,5340]/[LCM of 390,120]= 6/1560
Therefore, the GCF of 906/390,5340/120 is 6/1560.
To find the highest common factor of 906,5340, we have to find the factors of both numbers and list the highest common factor.
The factors of 906 are 1, 2, 3, 6, 151, 302, 453, 906
The factors of 5340 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 89, 178, 267, 356, 445, 534, 890, 1068, 1335, 1780, 2670, 5340
The HCF of 906,5340 is 6.
Lets's calculate GCF of 906,5340
| 2 | 906, 5340 |
| 3 | 453, 2670 |
| 151, 890 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 906,5340 By Matching Biggest Common Factor Method
Now, list down the factors of 906
:1,2,3,6,151,302,453,906
Now, list down the factors of 5340
:1,2,3,4,5,6,10,12,15,20,30,60,89,178,267,356,445,534,890,1068,1335,1780,2670,5340
Greatest Common Factor
We found the factors 906,5340 . The biggest common factor number is the GCF number.
So the greatest common factor 906,5340 is 6.
Lets's calculate LCM of 390,120
| 2 | 390, 120 |
| 3 | 195, 60 |
| 5 | 65, 20 |
| 13, 4 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 13 x 4 = 1560
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/1560
Therefore, the GCF of Fractions 906/390,5340/120 is 6/1560
Least Common Multiple of 390,120 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 390,120 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(390,120) = 30
common factors(in case of two or more numbers have common factors) = 1
GCF(390,120) x common factors =30 x 1 = 30
LCM(390,120) = ( 390 × 120 ) / 30
LCM(390,120) = 46800 / 30
LCM(390,120) = 1560
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FAQs on GCF of Fractions of 906/390, 5340/120
1. What is the HCF of 906,5340?
The HCF of 906,5340 is 6
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 906/390, 5340/120?
Answer: GCF of Numerators as per given numbers 906/390, 5340/120 is
GCF of Numerators i.e. for 906,5340 is 6
LCM of denominators i.e. for 390,120 is 1560.
Thus, GCF of Fractions is 6/1560.Finally, GCF of Fractions for 906/390, 5340/120 is 6/1560.