GCF of 455/432, 420/574
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 455/432, 420/574 i.e 35/123984 easily. The following is the detailed procedure to determine the greatest common factor of fractions 455/432, 420/574.
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 455/432,420/574?
Given fractions are 455/432,420/574
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 455/432,420/574, numerators are 455,420
Denominators are 432,574
The GCF of 455,420 is 35 .
LCM of 432,574 is 123984.
The greatest common factor of 455/432,420/574 = [GCF of 455,420]/[LCM of 432,574]= 35/123984
Therefore, the GCF of 455/432,420/574 is 35/123984.
To find the highest common factor of 455,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 455 are 1, 5, 7, 13, 35, 65, 91, 455
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 455,420 is 35.
Lets's calculate GCF of 455,420
| 5 | 455, 420 |
| 7 | 91, 84 |
| 13, 12 |
∴ So the GCF of the given numbers is 5 x 7 = 35
Greatest Common Factor of 455,420 By Matching Biggest Common Factor Method
Now, list down the factors of 455
:1,5,7,13,35,65,91,455
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 455,420 . The biggest common factor number is the GCF number.
So the greatest common factor 455,420 is 35.
Lets's calculate LCM of 432,574
| 2 | 432, 574 |
| 216, 287 |
∴ So the LCM of the given numbers is 2 x 216 x 287 = 123984
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 35/123984
Therefore, the GCF of Fractions 455/432,420/574 is 35/123984
Least Common Multiple of 432,574 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 432,574 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(432,574) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(432,574) x common factors =2 x 1 = 2
LCM(432,574) = ( 432 × 574 ) / 2
LCM(432,574) = 247968 / 2
LCM(432,574) = 123984
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FAQs on GCF of Fractions of 455/432, 420/574
1. What is the HCF of 455,420?
The HCF of 455,420 is 35
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 455/432, 420/574?
Answer: GCF of Numerators as per given numbers 455/432, 420/574 is
GCF of Numerators i.e. for 455,420 is 35
LCM of denominators i.e. for 432,574 is 123984.
Thus, GCF of Fractions is 35/123984.Finally, GCF of Fractions for 455/432, 420/574 is 35/123984.