GCF of 448/49, 217/474
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 448/49, 217/474 i.e 7/23226 easily. The following is the detailed procedure to determine the greatest common factor of fractions 448/49, 217/474.
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 448/49,217/474?
Given fractions are 448/49,217/474
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 448/49,217/474, numerators are 448,217
Denominators are 49,474
The GCF of 448,217 is 7 .
LCM of 49,474 is 23226.
The greatest common factor of 448/49,217/474 = [GCF of 448,217]/[LCM of 49,474]= 7/23226
Therefore, the GCF of 448/49,217/474 is 7/23226.
To find the highest common factor of 448,217, we have to find the factors of both numbers and list the highest common factor.
The factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448
The factors of 217 are 1, 7, 31, 217
The HCF of 448,217 is 7.
Lets's calculate GCF of 448,217
| 7 | 448, 217 |
| 64, 31 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 448,217 By Matching Biggest Common Factor Method
Now, list down the factors of 448
:1,2,4,7,8,14,16,28,32,56,64,112,224,448
Now, list down the factors of 217
:1,7,31,217
Greatest Common Factor
We found the factors 448,217 . The biggest common factor number is the GCF number.
So the greatest common factor 448,217 is 7.
Lets's calculate LCM of 49,474
Given numbers has no common factors except 1. So, there LCM is their product i.e 23226
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/23226
Therefore, the GCF of Fractions 448/49,217/474 is 7/23226
Least Common Multiple of 49,474 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 49,474 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(49,474) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(49,474) x common factors =1 x 1 = 1
LCM(49,474) = ( 49 × 474 ) / 1
LCM(49,474) = 23226 / 1
LCM(49,474) = 23226
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FAQs on GCF of Fractions of 448/49, 217/474
1. What is the HCF of 448,217?
The HCF of 448,217 is 7
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 448/49, 217/474?
Answer: GCF of Numerators as per given numbers 448/49, 217/474 is
GCF of Numerators i.e. for 448,217 is 7
LCM of denominators i.e. for 49,474 is 23226.
Thus, GCF of Fractions is 7/23226.Finally, GCF of Fractions for 448/49, 217/474 is 7/23226.