GCF of 46/420, 529/159
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 46/420, 529/159 i.e 23/22260 easily. The following is the detailed procedure to determine the greatest common factor of fractions 46/420, 529/159.
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 46/420,529/159?
Given fractions are 46/420,529/159
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 46/420,529/159, numerators are 46,529
Denominators are 420,159
The GCF of 46,529 is 23 .
LCM of 420,159 is 22260.
The greatest common factor of 46/420,529/159 = [GCF of 46,529]/[LCM of 420,159]= 23/22260
Therefore, the GCF of 46/420,529/159 is 23/22260.
To find the highest common factor of 46,529, we have to find the factors of both numbers and list the highest common factor.
The factors of 46 are 1, 2, 23, 46
The factors of 529 are 1, 23, 529
The HCF of 46,529 is 23.
Lets's calculate GCF of 46,529
| 23 | 46, 529 |
| 2, 23 |
∴ So the GCF of the given numbers is 23 = 23
Greatest Common Factor of 46,529 By Matching Biggest Common Factor Method
Now, list down the factors of 46
:1,2,23,46
Now, list down the factors of 529
:1,23,529
Greatest Common Factor
We found the factors 46,529 . The biggest common factor number is the GCF number.
So the greatest common factor 46,529 is 23.
Lets's calculate LCM of 420,159
| 3 | 420, 159 |
| 140, 53 |
∴ So the LCM of the given numbers is 3 x 140 x 53 = 22260
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 23/22260
Therefore, the GCF of Fractions 46/420,529/159 is 23/22260
Least Common Multiple of 420,159 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 420,159 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,159) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(420,159) x common factors =3 x 1 = 3
LCM(420,159) = ( 420 × 159 ) / 3
LCM(420,159) = 66780 / 3
LCM(420,159) = 22260
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FAQs on GCF of Fractions of 46/420, 529/159
1. What is the HCF of 46,529?
The HCF of 46,529 is 23
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 46/420, 529/159?
Answer: GCF of Numerators as per given numbers 46/420, 529/159 is
GCF of Numerators i.e. for 46,529 is 23
LCM of denominators i.e. for 420,159 is 22260.
Thus, GCF of Fractions is 23/22260.Finally, GCF of Fractions for 46/420, 529/159 is 23/22260.