GCF of 8/50, 38/77, 14/264, 616/288
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8/50, 38/77, 14/264, 616/288 i.e 2/554400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8/50, 38/77, 14/264, 616/288.
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 8/50,38/77,14/264,616/288?
Given fractions are 8/50,38/77,14/264,616/288
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 8/50,38/77,14/264,616/288, numerators are 8,38,14,616
Denominators are 50,77,264,288
The GCF of 8,38,14,616 is 2 .
LCM of 50,77,264,288 is 554400.
The greatest common factor of 8/50,38/77,14/264,616/288 = [GCF of 8,38,14,616]/[LCM of 50,77,264,288]= 2/554400
Therefore, the GCF of 8/50,38/77,14/264,616/288 is 2/554400.
To find the highest common factor of 8,38,14,616, we have to find the factors of both numbers and list the highest common factor.
The factors of 8 are 1, 2, 4, 8
The factors of 38 are 1, 2, 19, 38
The factors of 14 are 1, 2, 7, 14
The factors of 616 are 1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308, 616
The HCF of 8,38,14,616 is 2.
Lets's calculate GCF of 8,38,14,616
| 2 | 8, 38, 14, 616 |
| 4, 19, 7, 308 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 8,38,14,616 By Matching Biggest Common Factor Method
Now, list down the factors of 8
:1,2,4,8
Now, list down the factors of 38
:1,2,19,38
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 616
:1,2,4,7,8,11,14,22,28,44,56,77,88,154,308,616
Greatest Common Factor
We found the factors 8,38,14,616 . The biggest common factor number is the GCF number.
So the greatest common factor 8,38,14,616 is 2.
Lets's calculate LCM of 50,77,264,288
| 2 | 50, 77, 264, 288 |
| 2 | 25, 77, 132, 144 |
| 2 | 25, 77, 66, 72 |
| 3 | 25, 77, 33, 36 |
| 11 | 25, 77, 11, 12 |
| 25, 7, 1, 12 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 11 x 25 x 7 x 1 x 12 = 554400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/554400
Therefore, the GCF of Fractions 8/50,38/77,14/264,616/288 is 2/554400
Least Common Multiple of 50,77,264,288 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 50,77,264,288 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(50,77,264,288) = 1
common factors(in case of two or more numbers have common factors) = 528
GCF(50,77,264,288) x common factors =1 x 528 = 528
LCM(50,77,264,288) = ( 50 × 77 × 264 × 288 ) / 528
LCM(50,77,264,288) = 292723200 / 528
LCM(50,77,264,288) = 554400
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FAQs on GCF of Fractions of 8/50, 38/77, 14/264, 616/288
1. What is the HCF of 8,38,14,616?
The HCF of 8,38,14,616 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 8/50, 38/77, 14/264, 616/288?
Answer: GCF of Numerators as per given numbers 8/50, 38/77, 14/264, 616/288 is
GCF of Numerators i.e. for 8,38,14,616 is 2
LCM of denominators i.e. for 50,77,264,288 is 554400.
Thus, GCF of Fractions is 2/554400.Finally, GCF of Fractions for 8/50, 38/77, 14/264, 616/288 is 2/554400.