GCF of 74/28, 40/67, 65/16, 16/38
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 74/28, 40/67, 65/16, 16/38 i.e 1/142576 easily. The following is the detailed procedure to determine the greatest common factor of fractions 74/28, 40/67, 65/16, 16/38.
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 74/28,40/67,65/16,16/38?
Given fractions are 74/28,40/67,65/16,16/38
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 74/28,40/67,65/16,16/38, numerators are 74,40,65,16
Denominators are 28,67,16,38
The GCF of 74,40,65,16 is 1 .
LCM of 28,67,16,38 is 142576.
The greatest common factor of 74/28,40/67,65/16,16/38 = [GCF of 74,40,65,16]/[LCM of 28,67,16,38]= 1/142576
Therefore, the GCF of 74/28,40/67,65/16,16/38 is 1/142576.
To find the highest common factor of 74,40,65,16, we have to find the factors of both numbers and list the highest common factor.
The factors of 74 are 1, 2, 37, 74
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 65 are 1, 5, 13, 65
The factors of 16 are 1, 2, 4, 8, 16
The HCF of 74,40,65,16 is 1.
Lets's calculate GCF of 74,40,65,16
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 74,40,65,16 By Matching Biggest Common Factor Method
Now, list down the factors of 74
:1,2,37,74
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 65
:1,5,13,65
Now, list down the factors of 16
:1,2,4,8,16
Greatest Common Factor
We found the factors 74,40,65,16 . The biggest common factor number is the GCF number.
So the greatest common factor 74,40,65,16 is 1.
Lets's calculate LCM of 28,67,16,38
| 2 | 28, 67, 16, 38 |
| 2 | 14, 67, 8, 19 |
| 7, 67, 4, 19 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 67 x 4 x 19 = 142576
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/142576
Therefore, the GCF of Fractions 74/28,40/67,65/16,16/38 is 1/142576
Least Common Multiple of 28,67,16,38 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 28,67,16,38 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(28,67,16,38) = 1
common factors(in case of two or more numbers have common factors) = 8
GCF(28,67,16,38) x common factors =1 x 8 = 8
LCM(28,67,16,38) = ( 28 × 67 × 16 × 38 ) / 8
LCM(28,67,16,38) = 1140608 / 8
LCM(28,67,16,38) = 142576
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 74/28, 40/67, 65/16, 16/38
1. What is the HCF of 74,40,65,16?
The HCF of 74,40,65,16 is 1
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 74/28, 40/67, 65/16, 16/38?
Answer: GCF of Numerators as per given numbers 74/28, 40/67, 65/16, 16/38 is
GCF of Numerators i.e. for 74,40,65,16 is 1
LCM of denominators i.e. for 28,67,16,38 is 142576.
Thus, GCF of Fractions is 1/142576.Finally, GCF of Fractions for 74/28, 40/67, 65/16, 16/38 is 1/142576.