GCF of 403/649, 217/228
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 403/649, 217/228 i.e 31/147972 easily. The following is the detailed procedure to determine the greatest common factor of fractions 403/649, 217/228.
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 403/649,217/228?
Given fractions are 403/649,217/228
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 403/649,217/228, numerators are 403,217
Denominators are 649,228
The GCF of 403,217 is 31 .
LCM of 649,228 is 147972.
The greatest common factor of 403/649,217/228 = [GCF of 403,217]/[LCM of 649,228]= 31/147972
Therefore, the GCF of 403/649,217/228 is 31/147972.
To find the highest common factor of 403,217, we have to find the factors of both numbers and list the highest common factor.
The factors of 403 are 1, 13, 31, 403
The factors of 217 are 1, 7, 31, 217
The HCF of 403,217 is 31.
Lets's calculate GCF of 403,217
| 31 | 403, 217 |
| 13, 7 |
∴ So the GCF of the given numbers is 31 = 31
Greatest Common Factor of 403,217 By Matching Biggest Common Factor Method
Now, list down the factors of 403
:1,13,31,403
Now, list down the factors of 217
:1,7,31,217
Greatest Common Factor
We found the factors 403,217 . The biggest common factor number is the GCF number.
So the greatest common factor 403,217 is 31.
Lets's calculate LCM of 649,228
Given numbers has no common factors except 1. So, there LCM is their product i.e 147972
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/147972
Therefore, the GCF of Fractions 403/649,217/228 is 31/147972
Least Common Multiple of 649,228 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 649,228 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(649,228) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(649,228) x common factors =1 x 1 = 1
LCM(649,228) = ( 649 × 228 ) / 1
LCM(649,228) = 147972 / 1
LCM(649,228) = 147972
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FAQs on GCF of Fractions of 403/649, 217/228
1. What is the HCF of 403,217?
The HCF of 403,217 is 31
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 403/649, 217/228?
Answer: GCF of Numerators as per given numbers 403/649, 217/228 is
GCF of Numerators i.e. for 403,217 is 31
LCM of denominators i.e. for 649,228 is 147972.
Thus, GCF of Fractions is 31/147972.Finally, GCF of Fractions for 403/649, 217/228 is 31/147972.