GCF of 81/84, 84/90, 39/84, 10/69
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 81/84, 84/90, 39/84, 10/69 i.e 1/28980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 81/84, 84/90, 39/84, 10/69.
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 81/84,84/90,39/84,10/69?
Given fractions are 81/84,84/90,39/84,10/69
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 81/84,84/90,39/84,10/69, numerators are 81,84,39,10
Denominators are 84,90,84,69
The GCF of 81,84,39,10 is 1 .
LCM of 84,90,84,69 is 28980.
The greatest common factor of 81/84,84/90,39/84,10/69 = [GCF of 81,84,39,10]/[LCM of 84,90,84,69]= 1/28980
Therefore, the GCF of 81/84,84/90,39/84,10/69 is 1/28980.
To find the highest common factor of 81,84,39,10, we have to find the factors of both numbers and list the highest common factor.
The factors of 81 are 1, 3, 9, 27, 81
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 39 are 1, 3, 13, 39
The factors of 10 are 1, 2, 5, 10
The HCF of 81,84,39,10 is 1.
Lets's calculate GCF of 81,84,39,10
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 81,84,39,10 By Matching Biggest Common Factor Method
Now, list down the factors of 81
:1,3,9,27,81
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
Now, list down the factors of 39
:1,3,13,39
Now, list down the factors of 10
:1,2,5,10
Greatest Common Factor
We found the factors 81,84,39,10 . The biggest common factor number is the GCF number.
So the greatest common factor 81,84,39,10 is 1.
Lets's calculate LCM of 84,90,84,69
| 2 | 84, 90, 84, 69 |
| 2 | 42, 45, 42, 69 |
| 3 | 21, 45, 21, 69 |
| 7 | 7, 15, 7, 23 |
| 1, 15, 1, 23 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 1 x 15 x 1 x 23 = 28980
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/28980
Therefore, the GCF of Fractions 81/84,84/90,39/84,10/69 is 1/28980
Least Common Multiple of 84,90,84,69 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 84,90,84,69 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,90,84,69) = 3
common factors(in case of two or more numbers have common factors) = 504
GCF(84,90,84,69) x common factors =3 x 504 = 1512
LCM(84,90,84,69) = ( 84 × 90 × 84 × 69 ) / 1512
LCM(84,90,84,69) = 43817760 / 1512
LCM(84,90,84,69) = 28980
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 81/84, 84/90, 39/84, 10/69
1. What is the HCF of 81,84,39,10?
The HCF of 81,84,39,10 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 81/84, 84/90, 39/84, 10/69?
Answer: GCF of Numerators as per given numbers 81/84, 84/90, 39/84, 10/69 is
GCF of Numerators i.e. for 81,84,39,10 is 1
LCM of denominators i.e. for 84,90,84,69 is 28980.
Thus, GCF of Fractions is 1/28980.Finally, GCF of Fractions for 81/84, 84/90, 39/84, 10/69 is 1/28980.