GCF of 402/13, 450/520
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 402/13, 450/520 i.e 6/520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 402/13, 450/520.
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 402/13,450/520?
Given fractions are 402/13,450/520
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 402/13,450/520, numerators are 402,450
Denominators are 13,520
The GCF of 402,450 is 6 .
LCM of 13,520 is 520.
The greatest common factor of 402/13,450/520 = [GCF of 402,450]/[LCM of 13,520]= 6/520
Therefore, the GCF of 402/13,450/520 is 6/520.
To find the highest common factor of 402,450, we have to find the factors of both numbers and list the highest common factor.
The factors of 402 are 1, 2, 3, 6, 67, 134, 201, 402
The factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
The HCF of 402,450 is 6.
Lets's calculate GCF of 402,450
| 2 | 402, 450 |
| 3 | 201, 225 |
| 67, 75 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 402,450 By Matching Biggest Common Factor Method
Now, list down the factors of 402
:1,2,3,6,67,134,201,402
Now, list down the factors of 450
:1,2,3,5,6,9,10,15,18,25,30,45,50,75,90,150,225,450
Greatest Common Factor
We found the factors 402,450 . The biggest common factor number is the GCF number.
So the greatest common factor 402,450 is 6.
Lets's calculate LCM of 13,520
| 13 | 13, 520 |
| 1, 40 |
∴ So the LCM of the given numbers is 13 x 1 x 40 = 520
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/520
Therefore, the GCF of Fractions 402/13,450/520 is 6/520
Least Common Multiple of 13,520 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 13,520 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(13,520) = 13
common factors(in case of two or more numbers have common factors) = 1
GCF(13,520) x common factors =13 x 1 = 13
LCM(13,520) = ( 13 × 520 ) / 13
LCM(13,520) = 6760 / 13
LCM(13,520) = 520
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FAQs on GCF of Fractions of 402/13, 450/520
1. What is the HCF of 402,450?
The HCF of 402,450 is 6
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 402/13, 450/520?
Answer: GCF of Numerators as per given numbers 402/13, 450/520 is
GCF of Numerators i.e. for 402,450 is 6
LCM of denominators i.e. for 13,520 is 520.
Thus, GCF of Fractions is 6/520.Finally, GCF of Fractions for 402/13, 450/520 is 6/520.