GCF of 112/49, 163/420
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 112/49, 163/420 i.e 1/2940 easily. The following is the detailed procedure to determine the greatest common factor of fractions 112/49, 163/420.
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 112/49,163/420?
Given fractions are 112/49,163/420
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 112/49,163/420, numerators are 112,163
Denominators are 49,420
The GCF of 112,163 is 1 .
LCM of 49,420 is 2940.
The greatest common factor of 112/49,163/420 = [GCF of 112,163]/[LCM of 49,420]= 1/2940
Therefore, the GCF of 112/49,163/420 is 1/2940.
To find the highest common factor of 112,163, we have to find the factors of both numbers and list the highest common factor.
The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
The factors of 163 are 1, 163
The HCF of 112,163 is 1.
Lets's calculate GCF of 112,163
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 112,163 By Matching Biggest Common Factor Method
Now, list down the factors of 112
:1,2,4,7,8,14,16,28,56,112
Now, list down the factors of 163
:1,163
Greatest Common Factor
We found the factors 112,163 . The biggest common factor number is the GCF number.
So the greatest common factor 112,163 is 1.
Lets's calculate LCM of 49,420
| 7 | 49, 420 |
| 7, 60 |
∴ So the LCM of the given numbers is 7 x 7 x 60 = 2940
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2940
Therefore, the GCF of Fractions 112/49,163/420 is 1/2940
Least Common Multiple of 49,420 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 49,420 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(49,420) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(49,420) x common factors =7 x 1 = 7
LCM(49,420) = ( 49 × 420 ) / 7
LCM(49,420) = 20580 / 7
LCM(49,420) = 2940
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FAQs on GCF of Fractions of 112/49, 163/420
1. What is the HCF of 112,163?
The HCF of 112,163 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 112/49, 163/420?
Answer: GCF of Numerators as per given numbers 112/49, 163/420 is
GCF of Numerators i.e. for 112,163 is 1
LCM of denominators i.e. for 49,420 is 2940.
Thus, GCF of Fractions is 1/2940.Finally, GCF of Fractions for 112/49, 163/420 is 1/2940.