GCF of 420/74, 434/458
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 420/74, 434/458 i.e 14/16946 easily. The following is the detailed procedure to determine the greatest common factor of fractions 420/74, 434/458.
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 420/74,434/458?
Given fractions are 420/74,434/458
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 420/74,434/458, numerators are 420,434
Denominators are 74,458
The GCF of 420,434 is 14 .
LCM of 74,458 is 16946.
The greatest common factor of 420/74,434/458 = [GCF of 420,434]/[LCM of 74,458]= 14/16946
Therefore, the GCF of 420/74,434/458 is 14/16946.
To find the highest common factor of 420,434, we have to find the factors of both numbers and list the highest common factor.
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 factors of 434 are 1, 2, 7, 14, 31, 62, 217, 434
The HCF of 420,434 is 14.
Lets's calculate GCF of 420,434
| 2 | 420, 434 |
| 7 | 210, 217 |
| 30, 31 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 420,434 By Matching Biggest Common Factor Method
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
Now, list down the factors of 434
:1,2,7,14,31,62,217,434
Greatest Common Factor
We found the factors 420,434 . The biggest common factor number is the GCF number.
So the greatest common factor 420,434 is 14.
Lets's calculate LCM of 74,458
| 2 | 74, 458 |
| 37, 229 |
∴ So the LCM of the given numbers is 2 x 37 x 229 = 16946
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/16946
Therefore, the GCF of Fractions 420/74,434/458 is 14/16946
Least Common Multiple of 74,458 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 74,458 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,458) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(74,458) x common factors =2 x 1 = 2
LCM(74,458) = ( 74 × 458 ) / 2
LCM(74,458) = 33892 / 2
LCM(74,458) = 16946
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FAQs on GCF of Fractions of 420/74, 434/458
1. What is the HCF of 420,434?
The HCF of 420,434 is 14
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 420/74, 434/458?
Answer: GCF of Numerators as per given numbers 420/74, 434/458 is
GCF of Numerators i.e. for 420,434 is 14
LCM of denominators i.e. for 74,458 is 16946.
Thus, GCF of Fractions is 14/16946.Finally, GCF of Fractions for 420/74, 434/458 is 14/16946.