GCF of 38/362, 5678/1506
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 38/362, 5678/1506 i.e 2/272586 easily. The following is the detailed procedure to determine the greatest common factor of fractions 38/362, 5678/1506.
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 38/362,5678/1506?
Given fractions are 38/362,5678/1506
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 38/362,5678/1506, numerators are 38,5678
Denominators are 362,1506
The GCF of 38,5678 is 2 .
LCM of 362,1506 is 272586.
The greatest common factor of 38/362,5678/1506 = [GCF of 38,5678]/[LCM of 362,1506]= 2/272586
Therefore, the GCF of 38/362,5678/1506 is 2/272586.
To find the highest common factor of 38,5678, we have to find the factors of both numbers and list the highest common factor.
The factors of 38 are 1, 2, 19, 38
The factors of 5678 are 1, 2, 17, 34, 167, 334, 2839, 5678
The HCF of 38,5678 is 2.
Lets's calculate GCF of 38,5678
| 2 | 38, 5678 |
| 19, 2839 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 38,5678 By Matching Biggest Common Factor Method
Now, list down the factors of 38
:1,2,19,38
Now, list down the factors of 5678
:1,2,17,34,167,334,2839,5678
Greatest Common Factor
We found the factors 38,5678 . The biggest common factor number is the GCF number.
So the greatest common factor 38,5678 is 2.
Lets's calculate LCM of 362,1506
| 2 | 362, 1506 |
| 181, 753 |
∴ So the LCM of the given numbers is 2 x 181 x 753 = 272586
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/272586
Therefore, the GCF of Fractions 38/362,5678/1506 is 2/272586
Least Common Multiple of 362,1506 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 362,1506 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(362,1506) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(362,1506) x common factors =2 x 1 = 2
LCM(362,1506) = ( 362 × 1506 ) / 2
LCM(362,1506) = 545172 / 2
LCM(362,1506) = 272586
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FAQs on GCF of Fractions of 38/362, 5678/1506
1. What is the HCF of 38,5678?
The HCF of 38,5678 is 2
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 38/362, 5678/1506?
Answer: GCF of Numerators as per given numbers 38/362, 5678/1506 is
GCF of Numerators i.e. for 38,5678 is 2
LCM of denominators i.e. for 362,1506 is 272586.
Thus, GCF of Fractions is 2/272586.Finally, GCF of Fractions for 38/362, 5678/1506 is 2/272586.