GCF of 1218/15, 1456/635
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1218/15, 1456/635 i.e 14/1905 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1218/15, 1456/635.
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 1218/15,1456/635?
Given fractions are 1218/15,1456/635
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 1218/15,1456/635, numerators are 1218,1456
Denominators are 15,635
The GCF of 1218,1456 is 14 .
LCM of 15,635 is 1905.
The greatest common factor of 1218/15,1456/635 = [GCF of 1218,1456]/[LCM of 15,635]= 14/1905
Therefore, the GCF of 1218/15,1456/635 is 14/1905.
To find the highest common factor of 1218,1456, we have to find the factors of both numbers and list the highest common factor.
The factors of 1218 are 1, 2, 3, 6, 7, 14, 21, 29, 42, 58, 87, 174, 203, 406, 609, 1218
The factors of 1456 are 1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 52, 56, 91, 104, 112, 182, 208, 364, 728, 1456
The HCF of 1218,1456 is 14.
Lets's calculate GCF of 1218,1456
| 2 | 1218, 1456 |
| 7 | 609, 728 |
| 87, 104 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 1218,1456 By Matching Biggest Common Factor Method
Now, list down the factors of 1218
:1,2,3,6,7,14,21,29,42,58,87,174,203,406,609,1218
Now, list down the factors of 1456
:1,2,4,7,8,13,14,16,26,28,52,56,91,104,112,182,208,364,728,1456
Greatest Common Factor
We found the factors 1218,1456 . The biggest common factor number is the GCF number.
So the greatest common factor 1218,1456 is 14.
Lets's calculate LCM of 15,635
| 5 | 15, 635 |
| 3, 127 |
∴ So the LCM of the given numbers is 5 x 3 x 127 = 1905
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/1905
Therefore, the GCF of Fractions 1218/15,1456/635 is 14/1905
Least Common Multiple of 15,635 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 15,635 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(15,635) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(15,635) x common factors =5 x 1 = 5
LCM(15,635) = ( 15 × 635 ) / 5
LCM(15,635) = 9525 / 5
LCM(15,635) = 1905
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FAQs on GCF of Fractions of 1218/15, 1456/635
1. What is the HCF of 1218,1456?
The HCF of 1218,1456 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 1218/15, 1456/635?
Answer: GCF of Numerators as per given numbers 1218/15, 1456/635 is
GCF of Numerators i.e. for 1218,1456 is 14
LCM of denominators i.e. for 15,635 is 1905.
Thus, GCF of Fractions is 14/1905.Finally, GCF of Fractions for 1218/15, 1456/635 is 14/1905.