GCF of 578/312, 420/124
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 578/312, 420/124 i.e 2/9672 easily. The following is the detailed procedure to determine the greatest common factor of fractions 578/312, 420/124.
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 578/312,420/124?
Given fractions are 578/312,420/124
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 578/312,420/124, numerators are 578,420
Denominators are 312,124
The GCF of 578,420 is 2 .
LCM of 312,124 is 9672.
The greatest common factor of 578/312,420/124 = [GCF of 578,420]/[LCM of 312,124]= 2/9672
Therefore, the GCF of 578/312,420/124 is 2/9672.
To find the highest common factor of 578,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 578 are 1, 2, 17, 34, 289, 578
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 578,420 is 2.
Lets's calculate GCF of 578,420
| 2 | 578, 420 |
| 289, 210 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 578,420 By Matching Biggest Common Factor Method
Now, list down the factors of 578
:1,2,17,34,289,578
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 578,420 . The biggest common factor number is the GCF number.
So the greatest common factor 578,420 is 2.
Lets's calculate LCM of 312,124
| 2 | 312, 124 |
| 2 | 156, 62 |
| 78, 31 |
∴ So the LCM of the given numbers is 2 x 2 x 78 x 31 = 9672
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/9672
Therefore, the GCF of Fractions 578/312,420/124 is 2/9672
Least Common Multiple of 312,124 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 312,124 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(312,124) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(312,124) x common factors =4 x 1 = 4
LCM(312,124) = ( 312 × 124 ) / 4
LCM(312,124) = 38688 / 4
LCM(312,124) = 9672
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FAQs on GCF of Fractions of 578/312, 420/124
1. What is the HCF of 578,420?
The HCF of 578,420 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 578/312, 420/124?
Answer: GCF of Numerators as per given numbers 578/312, 420/124 is
GCF of Numerators i.e. for 578,420 is 2
LCM of denominators i.e. for 312,124 is 9672.
Thus, GCF of Fractions is 2/9672.Finally, GCF of Fractions for 578/312, 420/124 is 2/9672.