GCF of 468/504, 214/168
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 468/504, 214/168 i.e 2/504 easily. The following is the detailed procedure to determine the greatest common factor of fractions 468/504, 214/168.
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 468/504,214/168?
Given fractions are 468/504,214/168
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 468/504,214/168, numerators are 468,214
Denominators are 504,168
The GCF of 468,214 is 2 .
LCM of 504,168 is 504.
The greatest common factor of 468/504,214/168 = [GCF of 468,214]/[LCM of 504,168]= 2/504
Therefore, the GCF of 468/504,214/168 is 2/504.
To find the highest common factor of 468,214, we have to find the factors of both numbers and list the highest common factor.
The factors of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468
The factors of 214 are 1, 2, 107, 214
The HCF of 468,214 is 2.
Lets's calculate GCF of 468,214
| 2 | 468, 214 |
| 234, 107 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 468,214 By Matching Biggest Common Factor Method
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
Now, list down the factors of 214
:1,2,107,214
Greatest Common Factor
We found the factors 468,214 . The biggest common factor number is the GCF number.
So the greatest common factor 468,214 is 2.
Lets's calculate LCM of 504,168
| 2 | 504, 168 |
| 2 | 252, 84 |
| 2 | 126, 42 |
| 3 | 63, 21 |
| 7 | 7, 21 |
| 1, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 7 x 1 x 3 = 504
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/504
Therefore, the GCF of Fractions 468/504,214/168 is 2/504
Least Common Multiple of 504,168 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 504,168 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(504,168) = 168
common factors(in case of two or more numbers have common factors) = 1
GCF(504,168) x common factors =168 x 1 = 168
LCM(504,168) = ( 504 × 168 ) / 168
LCM(504,168) = 84672 / 168
LCM(504,168) = 504
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FAQs on GCF of Fractions of 468/504, 214/168
1. What is the HCF of 468,214?
The HCF of 468,214 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 468/504, 214/168?
Answer: GCF of Numerators as per given numbers 468/504, 214/168 is
GCF of Numerators i.e. for 468,214 is 2
LCM of denominators i.e. for 504,168 is 504.
Thus, GCF of Fractions is 2/504.Finally, GCF of Fractions for 468/504, 214/168 is 2/504.