GCF of 7738/154, 4240/5328
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7738/154, 4240/5328 i.e 106/410256 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7738/154, 4240/5328.
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 7738/154,4240/5328?
Given fractions are 7738/154,4240/5328
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 7738/154,4240/5328, numerators are 7738,4240
Denominators are 154,5328
The GCF of 7738,4240 is 106 .
LCM of 154,5328 is 410256.
The greatest common factor of 7738/154,4240/5328 = [GCF of 7738,4240]/[LCM of 154,5328]= 106/410256
Therefore, the GCF of 7738/154,4240/5328 is 106/410256.
To find the highest common factor of 7738,4240, we have to find the factors of both numbers and list the highest common factor.
The factors of 7738 are 1, 2, 53, 73, 106, 146, 3869, 7738
The factors of 4240 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 53, 80, 106, 212, 265, 424, 530, 848, 1060, 2120, 4240
The HCF of 7738,4240 is 106.
Lets's calculate GCF of 7738,4240
| 2 | 7738, 4240 |
| 53 | 3869, 2120 |
| 73, 40 |
∴ So the GCF of the given numbers is 2 x 53 = 106
Greatest Common Factor of 7738,4240 By Matching Biggest Common Factor Method
Now, list down the factors of 7738
:1,2,53,73,106,146,3869,7738
Now, list down the factors of 4240
:1,2,4,5,8,10,16,20,40,53,80,106,212,265,424,530,848,1060,2120,4240
Greatest Common Factor
We found the factors 7738,4240 . The biggest common factor number is the GCF number.
So the greatest common factor 7738,4240 is 106.
Lets's calculate LCM of 154,5328
| 2 | 154, 5328 |
| 77, 2664 |
∴ So the LCM of the given numbers is 2 x 77 x 2664 = 410256
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 106/410256
Therefore, the GCF of Fractions 7738/154,4240/5328 is 106/410256
Least Common Multiple of 154,5328 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 154,5328 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(154,5328) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(154,5328) x common factors =2 x 1 = 2
LCM(154,5328) = ( 154 × 5328 ) / 2
LCM(154,5328) = 820512 / 2
LCM(154,5328) = 410256
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FAQs on GCF of Fractions of 7738/154, 4240/5328
1. What is the HCF of 7738,4240?
The HCF of 7738,4240 is 106
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 7738/154, 4240/5328?
Answer: GCF of Numerators as per given numbers 7738/154, 4240/5328 is
GCF of Numerators i.e. for 7738,4240 is 106
LCM of denominators i.e. for 154,5328 is 410256.
Thus, GCF of Fractions is 106/410256.Finally, GCF of Fractions for 7738/154, 4240/5328 is 106/410256.