GCF of 29/84, 75/88, 78/12, 65/75
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 29/84, 75/88, 78/12, 65/75 i.e 1/46200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 29/84, 75/88, 78/12, 65/75.
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 29/84,75/88,78/12,65/75?
Given fractions are 29/84,75/88,78/12,65/75
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 29/84,75/88,78/12,65/75, numerators are 29,75,78,65
Denominators are 84,88,12,75
The GCF of 29,75,78,65 is 1 .
LCM of 84,88,12,75 is 46200.
The greatest common factor of 29/84,75/88,78/12,65/75 = [GCF of 29,75,78,65]/[LCM of 84,88,12,75]= 1/46200
Therefore, the GCF of 29/84,75/88,78/12,65/75 is 1/46200.
To find the highest common factor of 29,75,78,65, we have to find the factors of both numbers and list the highest common factor.
The factors of 29 are 1, 29
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
The factors of 65 are 1, 5, 13, 65
The HCF of 29,75,78,65 is 1.
Lets's calculate GCF of 29,75,78,65
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 29,75,78,65 By Matching Biggest Common Factor Method
Now, list down the factors of 29
:1,29
Now, list down the factors of 75
:1,3,5,15,25,75
Now, list down the factors of 78
:1,2,3,6,13,26,39,78
Now, list down the factors of 65
:1,5,13,65
Greatest Common Factor
We found the factors 29,75,78,65 . The biggest common factor number is the GCF number.
So the greatest common factor 29,75,78,65 is 1.
Lets's calculate LCM of 84,88,12,75
| 2 | 84, 88, 12, 75 |
| 2 | 42, 44, 6, 75 |
| 3 | 21, 22, 3, 75 |
| 7, 22, 1, 25 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 22 x 1 x 25 = 46200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/46200
Therefore, the GCF of Fractions 29/84,75/88,78/12,65/75 is 1/46200
Least Common Multiple of 84,88,12,75 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 84,88,12,75 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,88,12,75) = 1
common factors(in case of two or more numbers have common factors) = 144
GCF(84,88,12,75) x common factors =1 x 144 = 144
LCM(84,88,12,75) = ( 84 × 88 × 12 × 75 ) / 144
LCM(84,88,12,75) = 6652800 / 144
LCM(84,88,12,75) = 46200
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 29/84, 75/88, 78/12, 65/75
1. What is the HCF of 29,75,78,65?
The HCF of 29,75,78,65 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 29/84, 75/88, 78/12, 65/75?
Answer: GCF of Numerators as per given numbers 29/84, 75/88, 78/12, 65/75 is
GCF of Numerators i.e. for 29,75,78,65 is 1
LCM of denominators i.e. for 84,88,12,75 is 46200.
Thus, GCF of Fractions is 1/46200.Finally, GCF of Fractions for 29/84, 75/88, 78/12, 65/75 is 1/46200.