GCF of 414/78, 116/39, 468/21
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 414/78, 116/39, 468/21 i.e 2/546 easily. The following is the detailed procedure to determine the greatest common factor of fractions 414/78, 116/39, 468/21.
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 414/78,116/39,468/21?
Given fractions are 414/78,116/39,468/21
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 414/78,116/39,468/21, numerators are 414,116,468
Denominators are 78,39,21
The GCF of 414,116,468 is 2 .
LCM of 78,39,21 is 546.
The greatest common factor of 414/78,116/39,468/21 = [GCF of 414,116,468]/[LCM of 78,39,21]= 2/546
Therefore, the GCF of 414/78,116/39,468/21 is 2/546.
To find the highest common factor of 414,116,468, we have to find the factors of both numbers and list the highest common factor.
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The factors of 116 are 1, 2, 4, 29, 58, 116
The factors of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468
The HCF of 414,116,468 is 2.
Lets's calculate GCF of 414,116,468
| 2 | 414, 116, 468 |
| 207, 58, 234 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 414,116,468 By Matching Biggest Common Factor Method
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Now, list down the factors of 116
:1,2,4,29,58,116
Now, list down the factors of 468
:1,2,3,4,6,9,12,13,18,26,36,39,52,78,117,156,234,468
Greatest Common Factor
We found the factors 414,116,468 . The biggest common factor number is the GCF number.
So the greatest common factor 414,116,468 is 2.
Lets's calculate LCM of 78,39,21
| 3 | 78, 39, 21 |
| 13 | 26, 13, 7 |
| 2, 1, 7 |
∴ So the LCM of the given numbers is 3 x 13 x 2 x 1 x 7 = 546
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/546
Therefore, the GCF of Fractions 414/78,116/39,468/21 is 2/546
Least Common Multiple of 78,39,21 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 78,39,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,39,21) = 3
common factors(in case of two or more numbers have common factors) = 39
GCF(78,39,21) x common factors =3 x 39 = 117
LCM(78,39,21) = ( 78 × 39 × 21 ) / 117
LCM(78,39,21) = 63882 / 117
LCM(78,39,21) = 546
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FAQs on GCF of Fractions of 414/78, 116/39, 468/21
1. What is the HCF of 414,116,468?
The HCF of 414,116,468 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 414/78, 116/39, 468/21?
Answer: GCF of Numerators as per given numbers 414/78, 116/39, 468/21 is
GCF of Numerators i.e. for 414,116,468 is 2
LCM of denominators i.e. for 78,39,21 is 546.
Thus, GCF of Fractions is 2/546.Finally, GCF of Fractions for 414/78, 116/39, 468/21 is 2/546.