GCF of 430/36, 105/1224
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 430/36, 105/1224 i.e 5/1224 easily. The following is the detailed procedure to determine the greatest common factor of fractions 430/36, 105/1224.
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 430/36,105/1224?
Given fractions are 430/36,105/1224
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 430/36,105/1224, numerators are 430,105
Denominators are 36,1224
The GCF of 430,105 is 5 .
LCM of 36,1224 is 1224.
The greatest common factor of 430/36,105/1224 = [GCF of 430,105]/[LCM of 36,1224]= 5/1224
Therefore, the GCF of 430/36,105/1224 is 5/1224.
To find the highest common factor of 430,105, we have to find the factors of both numbers and list the highest common factor.
The factors of 430 are 1, 2, 5, 10, 43, 86, 215, 430
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The HCF of 430,105 is 5.
Lets's calculate GCF of 430,105
| 5 | 430, 105 |
| 86, 21 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 430,105 By Matching Biggest Common Factor Method
Now, list down the factors of 430
:1,2,5,10,43,86,215,430
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Greatest Common Factor
We found the factors 430,105 . The biggest common factor number is the GCF number.
So the greatest common factor 430,105 is 5.
Lets's calculate LCM of 36,1224
| 2 | 36, 1224 |
| 2 | 18, 612 |
| 3 | 9, 306 |
| 3 | 3, 102 |
| 1, 34 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 1 x 34 = 1224
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/1224
Therefore, the GCF of Fractions 430/36,105/1224 is 5/1224
Least Common Multiple of 36,1224 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 36,1224 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(36,1224) = 36
common factors(in case of two or more numbers have common factors) = 1
GCF(36,1224) x common factors =36 x 1 = 36
LCM(36,1224) = ( 36 × 1224 ) / 36
LCM(36,1224) = 44064 / 36
LCM(36,1224) = 1224
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FAQs on GCF of Fractions of 430/36, 105/1224
1. What is the HCF of 430,105?
The HCF of 430,105 is 5
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 430/36, 105/1224?
Answer: GCF of Numerators as per given numbers 430/36, 105/1224 is
GCF of Numerators i.e. for 430,105 is 5
LCM of denominators i.e. for 36,1224 is 1224.
Thus, GCF of Fractions is 5/1224.Finally, GCF of Fractions for 430/36, 105/1224 is 5/1224.