GCF of 18/78, 76/78, 58/44, 84/22
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 18/78, 76/78, 58/44, 84/22 i.e 2/1716 easily. The following is the detailed procedure to determine the greatest common factor of fractions 18/78, 76/78, 58/44, 84/22.
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 18/78,76/78,58/44,84/22?
Given fractions are 18/78,76/78,58/44,84/22
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 18/78,76/78,58/44,84/22, numerators are 18,76,58,84
Denominators are 78,78,44,22
The GCF of 18,76,58,84 is 2 .
LCM of 78,78,44,22 is 1716.
The greatest common factor of 18/78,76/78,58/44,84/22 = [GCF of 18,76,58,84]/[LCM of 78,78,44,22]= 2/1716
Therefore, the GCF of 18/78,76/78,58/44,84/22 is 2/1716.
To find the highest common factor of 18,76,58,84, we have to find the factors of both numbers and list the highest common factor.
The factors of 18 are 1, 2, 3, 6, 9, 18
The factors of 76 are 1, 2, 4, 19, 38, 76
The factors of 58 are 1, 2, 29, 58
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The HCF of 18,76,58,84 is 2.
Lets's calculate GCF of 18,76,58,84
| 2 | 18, 76, 58, 84 |
| 9, 38, 29, 42 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 18,76,58,84 By Matching Biggest Common Factor Method
Now, list down the factors of 18
:1,2,3,6,9,18
Now, list down the factors of 76
:1,2,4,19,38,76
Now, list down the factors of 58
:1,2,29,58
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
Greatest Common Factor
We found the factors 18,76,58,84 . The biggest common factor number is the GCF number.
So the greatest common factor 18,76,58,84 is 2.
Lets's calculate LCM of 78,78,44,22
| 2 | 78, 78, 44, 22 |
| 3 | 39, 39, 22, 11 |
| 11 | 13, 13, 22, 11 |
| 13 | 13, 13, 2, 1 |
| 1, 1, 2, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 11 x 13 x 1 x 1 x 2 x 1 = 1716
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1716
Therefore, the GCF of Fractions 18/78,76/78,58/44,84/22 is 2/1716
Least Common Multiple of 78,78,44,22 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 78,78,44,22 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,78,44,22) = 2
common factors(in case of two or more numbers have common factors) = 1716
GCF(78,78,44,22) x common factors =2 x 1716 = 3432
LCM(78,78,44,22) = ( 78 × 78 × 44 × 22 ) / 3432
LCM(78,78,44,22) = 5889312 / 3432
LCM(78,78,44,22) = 1716
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 18/78, 76/78, 58/44, 84/22
1. What is the HCF of 18,76,58,84?
The HCF of 18,76,58,84 is 2
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 18/78, 76/78, 58/44, 84/22?
Answer: GCF of Numerators as per given numbers 18/78, 76/78, 58/44, 84/22 is
GCF of Numerators i.e. for 18,76,58,84 is 2
LCM of denominators i.e. for 78,78,44,22 is 1716.
Thus, GCF of Fractions is 2/1716.Finally, GCF of Fractions for 18/78, 76/78, 58/44, 84/22 is 2/1716.