GCF of 24/108, 84/678
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 24/108, 84/678 i.e 12/12204 easily. The following is the detailed procedure to determine the greatest common factor of fractions 24/108, 84/678.
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 24/108,84/678?
Given fractions are 24/108,84/678
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 24/108,84/678, numerators are 24,84
Denominators are 108,678
The GCF of 24,84 is 12 .
LCM of 108,678 is 12204.
The greatest common factor of 24/108,84/678 = [GCF of 24,84]/[LCM of 108,678]= 12/12204
Therefore, the GCF of 24/108,84/678 is 12/12204.
To find the highest common factor of 24,84, we have to find the factors of both numbers and list the highest common factor.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The HCF of 24,84 is 12.
Lets's calculate GCF of 24,84
| 2 | 24, 84 |
| 2 | 12, 42 |
| 3 | 6, 21 |
| 2, 7 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 24,84 By Matching Biggest Common Factor Method
Now, list down the factors of 24
:1,2,3,4,6,8,12,24
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 24,84 . The biggest common factor number is the GCF number.
So the greatest common factor 24,84 is 12.
Lets's calculate LCM of 108,678
| 2 | 108, 678 |
| 3 | 54, 339 |
| 18, 113 |
∴ So the LCM of the given numbers is 2 x 3 x 18 x 113 = 12204
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/12204
Therefore, the GCF of Fractions 24/108,84/678 is 12/12204
Least Common Multiple of 108,678 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 108,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(108,678) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(108,678) x common factors =6 x 1 = 6
LCM(108,678) = ( 108 × 678 ) / 6
LCM(108,678) = 73224 / 6
LCM(108,678) = 12204
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FAQs on GCF of Fractions of 24/108, 84/678
1. What is the HCF of 24,84?
The HCF of 24,84 is 12
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 24/108, 84/678?
Answer: GCF of Numerators as per given numbers 24/108, 84/678 is
GCF of Numerators i.e. for 24,84 is 12
LCM of denominators i.e. for 108,678 is 12204.
Thus, GCF of Fractions is 12/12204.Finally, GCF of Fractions for 24/108, 84/678 is 12/12204.