GCF of 28/42, 67/66, 75/74, 15/320
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 28/42, 67/66, 75/74, 15/320 i.e 1/2735040 easily. The following is the detailed procedure to determine the greatest common factor of fractions 28/42, 67/66, 75/74, 15/320.
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 28/42,67/66,75/74,15/320?
Given fractions are 28/42,67/66,75/74,15/320
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 28/42,67/66,75/74,15/320, numerators are 28,67,75,15
Denominators are 42,66,74,320
The GCF of 28,67,75,15 is 1 .
LCM of 42,66,74,320 is 2735040.
The greatest common factor of 28/42,67/66,75/74,15/320 = [GCF of 28,67,75,15]/[LCM of 42,66,74,320]= 1/2735040
Therefore, the GCF of 28/42,67/66,75/74,15/320 is 1/2735040.
To find the highest common factor of 28,67,75,15, we have to find the factors of both numbers and list the highest common factor.
The factors of 28 are 1, 2, 4, 7, 14, 28
The factors of 67 are 1, 67
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 15 are 1, 3, 5, 15
The HCF of 28,67,75,15 is 1.
Lets's calculate GCF of 28,67,75,15
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 28,67,75,15 By Matching Biggest Common Factor Method
Now, list down the factors of 28
:1,2,4,7,14,28
Now, list down the factors of 67
:1,67
Now, list down the factors of 75
:1,3,5,15,25,75
Now, list down the factors of 15
:1,3,5,15
Greatest Common Factor
We found the factors 28,67,75,15 . The biggest common factor number is the GCF number.
So the greatest common factor 28,67,75,15 is 1.
Lets's calculate LCM of 42,66,74,320
| 2 | 42, 66, 74, 320 |
| 3 | 21, 33, 37, 160 |
| 7, 11, 37, 160 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 11 x 37 x 160 = 2735040
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2735040
Therefore, the GCF of Fractions 28/42,67/66,75/74,15/320 is 1/2735040
Least Common Multiple of 42,66,74,320 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 42,66,74,320 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,66,74,320) = 2
common factors(in case of two or more numbers have common factors) = 12
GCF(42,66,74,320) x common factors =2 x 12 = 24
LCM(42,66,74,320) = ( 42 × 66 × 74 × 320 ) / 24
LCM(42,66,74,320) = 65640960 / 24
LCM(42,66,74,320) = 2735040
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FAQs on GCF of Fractions of 28/42, 67/66, 75/74, 15/320
1. What is the HCF of 28,67,75,15?
The HCF of 28,67,75,15 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 28/42, 67/66, 75/74, 15/320?
Answer: GCF of Numerators as per given numbers 28/42, 67/66, 75/74, 15/320 is
GCF of Numerators i.e. for 28,67,75,15 is 1
LCM of denominators i.e. for 42,66,74,320 is 2735040.
Thus, GCF of Fractions is 1/2735040.Finally, GCF of Fractions for 28/42, 67/66, 75/74, 15/320 is 1/2735040.