GCF of 238/520, 5678/3256
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 238/520, 5678/3256 i.e 34/211640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 238/520, 5678/3256.
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 238/520,5678/3256?
Given fractions are 238/520,5678/3256
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 238/520,5678/3256, numerators are 238,5678
Denominators are 520,3256
The GCF of 238,5678 is 34 .
LCM of 520,3256 is 211640.
The greatest common factor of 238/520,5678/3256 = [GCF of 238,5678]/[LCM of 520,3256]= 34/211640
Therefore, the GCF of 238/520,5678/3256 is 34/211640.
To find the highest common factor of 238,5678, we have to find the factors of both numbers and list the highest common factor.
The factors of 238 are 1, 2, 7, 14, 17, 34, 119, 238
The factors of 5678 are 1, 2, 17, 34, 167, 334, 2839, 5678
The HCF of 238,5678 is 34.
Lets's calculate GCF of 238,5678
| 2 | 238, 5678 |
| 17 | 119, 2839 |
| 7, 167 |
∴ So the GCF of the given numbers is 2 x 17 = 34
Greatest Common Factor of 238,5678 By Matching Biggest Common Factor Method
Now, list down the factors of 238
:1,2,7,14,17,34,119,238
Now, list down the factors of 5678
:1,2,17,34,167,334,2839,5678
Greatest Common Factor
We found the factors 238,5678 . The biggest common factor number is the GCF number.
So the greatest common factor 238,5678 is 34.
Lets's calculate LCM of 520,3256
| 2 | 520, 3256 |
| 2 | 260, 1628 |
| 2 | 130, 814 |
| 65, 407 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 65 x 407 = 211640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 34/211640
Therefore, the GCF of Fractions 238/520,5678/3256 is 34/211640
Least Common Multiple of 520,3256 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 520,3256 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(520,3256) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(520,3256) x common factors =8 x 1 = 8
LCM(520,3256) = ( 520 × 3256 ) / 8
LCM(520,3256) = 1693120 / 8
LCM(520,3256) = 211640
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FAQs on GCF of Fractions of 238/520, 5678/3256
1. What is the HCF of 238,5678?
The HCF of 238,5678 is 34
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 238/520, 5678/3256?
Answer: GCF of Numerators as per given numbers 238/520, 5678/3256 is
GCF of Numerators i.e. for 238,5678 is 34
LCM of denominators i.e. for 520,3256 is 211640.
Thus, GCF of Fractions is 34/211640.Finally, GCF of Fractions for 238/520, 5678/3256 is 34/211640.