GCF of 918/420, 7689/4260
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 918/420, 7689/4260 i.e 3/29820 easily. The following is the detailed procedure to determine the greatest common factor of fractions 918/420, 7689/4260.
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 918/420,7689/4260?
Given fractions are 918/420,7689/4260
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 918/420,7689/4260, numerators are 918,7689
Denominators are 420,4260
The GCF of 918,7689 is 3 .
LCM of 420,4260 is 29820.
The greatest common factor of 918/420,7689/4260 = [GCF of 918,7689]/[LCM of 420,4260]= 3/29820
Therefore, the GCF of 918/420,7689/4260 is 3/29820.
To find the highest common factor of 918,7689, we have to find the factors of both numbers and list the highest common factor.
The factors of 918 are 1, 2, 3, 6, 9, 17, 18, 27, 34, 51, 54, 102, 153, 306, 459, 918
The factors of 7689 are 1, 3, 11, 33, 233, 699, 2563, 7689
The HCF of 918,7689 is 3.
Lets's calculate GCF of 918,7689
| 3 | 918, 7689 |
| 306, 2563 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 918,7689 By Matching Biggest Common Factor Method
Now, list down the factors of 918
:1,2,3,6,9,17,18,27,34,51,54,102,153,306,459,918
Now, list down the factors of 7689
:1,3,11,33,233,699,2563,7689
Greatest Common Factor
We found the factors 918,7689 . The biggest common factor number is the GCF number.
So the greatest common factor 918,7689 is 3.
Lets's calculate LCM of 420,4260
| 2 | 420, 4260 |
| 2 | 210, 2130 |
| 3 | 105, 1065 |
| 5 | 35, 355 |
| 7, 71 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 7 x 71 = 29820
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/29820
Therefore, the GCF of Fractions 918/420,7689/4260 is 3/29820
Least Common Multiple of 420,4260 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 420,4260 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,4260) = 60
common factors(in case of two or more numbers have common factors) = 1
GCF(420,4260) x common factors =60 x 1 = 60
LCM(420,4260) = ( 420 × 4260 ) / 60
LCM(420,4260) = 1789200 / 60
LCM(420,4260) = 29820
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FAQs on GCF of Fractions of 918/420, 7689/4260
1. What is the HCF of 918,7689?
The HCF of 918,7689 is 3
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 918/420, 7689/4260?
Answer: GCF of Numerators as per given numbers 918/420, 7689/4260 is
GCF of Numerators i.e. for 918,7689 is 3
LCM of denominators i.e. for 420,4260 is 29820.
Thus, GCF of Fractions is 3/29820.Finally, GCF of Fractions for 918/420, 7689/4260 is 3/29820.