GCF of 427/14, 296/105
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 427/14, 296/105 i.e 1/210 easily. The following is the detailed procedure to determine the greatest common factor of fractions 427/14, 296/105.
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 427/14,296/105?
Given fractions are 427/14,296/105
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 427/14,296/105, numerators are 427,296
Denominators are 14,105
The GCF of 427,296 is 1 .
LCM of 14,105 is 210.
The greatest common factor of 427/14,296/105 = [GCF of 427,296]/[LCM of 14,105]= 1/210
Therefore, the GCF of 427/14,296/105 is 1/210.
To find the highest common factor of 427,296, we have to find the factors of both numbers and list the highest common factor.
The factors of 427 are 1, 7, 61, 427
The factors of 296 are 1, 2, 4, 8, 37, 74, 148, 296
The HCF of 427,296 is 1.
Lets's calculate GCF of 427,296
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 427,296 By Matching Biggest Common Factor Method
Now, list down the factors of 427
:1,7,61,427
Now, list down the factors of 296
:1,2,4,8,37,74,148,296
Greatest Common Factor
We found the factors 427,296 . The biggest common factor number is the GCF number.
So the greatest common factor 427,296 is 1.
Lets's calculate LCM of 14,105
| 7 | 14, 105 |
| 2, 15 |
∴ So the LCM of the given numbers is 7 x 2 x 15 = 210
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/210
Therefore, the GCF of Fractions 427/14,296/105 is 1/210
Least Common Multiple of 14,105 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 14,105 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,105) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(14,105) x common factors =7 x 1 = 7
LCM(14,105) = ( 14 × 105 ) / 7
LCM(14,105) = 1470 / 7
LCM(14,105) = 210
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FAQs on GCF of Fractions of 427/14, 296/105
1. What is the HCF of 427,296?
The HCF of 427,296 is 1
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 427/14, 296/105?
Answer: GCF of Numerators as per given numbers 427/14, 296/105 is
GCF of Numerators i.e. for 427,296 is 1
LCM of denominators i.e. for 14,105 is 210.
Thus, GCF of Fractions is 1/210.Finally, GCF of Fractions for 427/14, 296/105 is 1/210.