GCF of 417/39, 524/221
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 417/39, 524/221 i.e 1/663 easily. The following is the detailed procedure to determine the greatest common factor of fractions 417/39, 524/221.
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 417/39,524/221?
Given fractions are 417/39,524/221
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 417/39,524/221, numerators are 417,524
Denominators are 39,221
The GCF of 417,524 is 1 .
LCM of 39,221 is 663.
The greatest common factor of 417/39,524/221 = [GCF of 417,524]/[LCM of 39,221]= 1/663
Therefore, the GCF of 417/39,524/221 is 1/663.
To find the highest common factor of 417,524, we have to find the factors of both numbers and list the highest common factor.
The factors of 417 are 1, 3, 139, 417
The factors of 524 are 1, 2, 4, 131, 262, 524
The HCF of 417,524 is 1.
Lets's calculate GCF of 417,524
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 417,524 By Matching Biggest Common Factor Method
Now, list down the factors of 417
:1,3,139,417
Now, list down the factors of 524
:1,2,4,131,262,524
Greatest Common Factor
We found the factors 417,524 . The biggest common factor number is the GCF number.
So the greatest common factor 417,524 is 1.
Lets's calculate LCM of 39,221
| 13 | 39, 221 |
| 3, 17 |
∴ So the LCM of the given numbers is 13 x 3 x 17 = 663
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/663
Therefore, the GCF of Fractions 417/39,524/221 is 1/663
Least Common Multiple of 39,221 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 39,221 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(39,221) = 13
common factors(in case of two or more numbers have common factors) = 1
GCF(39,221) x common factors =13 x 1 = 13
LCM(39,221) = ( 39 × 221 ) / 13
LCM(39,221) = 8619 / 13
LCM(39,221) = 663
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FAQs on GCF of Fractions of 417/39, 524/221
1. What is the HCF of 417,524?
The HCF of 417,524 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 417/39, 524/221?
Answer: GCF of Numerators as per given numbers 417/39, 524/221 is
GCF of Numerators i.e. for 417,524 is 1
LCM of denominators i.e. for 39,221 is 663.
Thus, GCF of Fractions is 1/663.Finally, GCF of Fractions for 417/39, 524/221 is 1/663.