GCF of 28/77, 40/84, 24/32, 69/38
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 28/77, 40/84, 24/32, 69/38 i.e 1/140448 easily. The following is the detailed procedure to determine the greatest common factor of fractions 28/77, 40/84, 24/32, 69/38.
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 28/77,40/84,24/32,69/38?
Given fractions are 28/77,40/84,24/32,69/38
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 28/77,40/84,24/32,69/38, numerators are 28,40,24,69
Denominators are 77,84,32,38
The GCF of 28,40,24,69 is 1 .
LCM of 77,84,32,38 is 140448.
The greatest common factor of 28/77,40/84,24/32,69/38 = [GCF of 28,40,24,69]/[LCM of 77,84,32,38]= 1/140448
Therefore, the GCF of 28/77,40/84,24/32,69/38 is 1/140448.
To find the highest common factor of 28,40,24,69, 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 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
The factors of 69 are 1, 3, 23, 69
The HCF of 28,40,24,69 is 1.
Lets's calculate GCF of 28,40,24,69
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 28,40,24,69 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 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 24
:1,2,3,4,6,8,12,24
Now, list down the factors of 69
:1,3,23,69
Greatest Common Factor
We found the factors 28,40,24,69 . The biggest common factor number is the GCF number.
So the greatest common factor 28,40,24,69 is 1.
Lets's calculate LCM of 77,84,32,38
| 2 | 77, 84, 32, 38 |
| 2 | 77, 42, 16, 19 |
| 7 | 77, 21, 8, 19 |
| 11, 3, 8, 19 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 11 x 3 x 8 x 19 = 140448
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/140448
Therefore, the GCF of Fractions 28/77,40/84,24/32,69/38 is 1/140448
Least Common Multiple of 77,84,32,38 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 77,84,32,38 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,84,32,38) = 1
common factors(in case of two or more numbers have common factors) = 56
GCF(77,84,32,38) x common factors =1 x 56 = 56
LCM(77,84,32,38) = ( 77 × 84 × 32 × 38 ) / 56
LCM(77,84,32,38) = 7865088 / 56
LCM(77,84,32,38) = 140448
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 28/77, 40/84, 24/32, 69/38
1. What is the HCF of 28,40,24,69?
The HCF of 28,40,24,69 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 28/77, 40/84, 24/32, 69/38?
Answer: GCF of Numerators as per given numbers 28/77, 40/84, 24/32, 69/38 is
GCF of Numerators i.e. for 28,40,24,69 is 1
LCM of denominators i.e. for 77,84,32,38 is 140448.
Thus, GCF of Fractions is 1/140448.Finally, GCF of Fractions for 28/77, 40/84, 24/32, 69/38 is 1/140448.