GCF of 3410/472, 4205/964
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3410/472, 4205/964 i.e 5/113752 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3410/472, 4205/964.
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 3410/472,4205/964?
Given fractions are 3410/472,4205/964
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 3410/472,4205/964, numerators are 3410,4205
Denominators are 472,964
The GCF of 3410,4205 is 5 .
LCM of 472,964 is 113752.
The greatest common factor of 3410/472,4205/964 = [GCF of 3410,4205]/[LCM of 472,964]= 5/113752
Therefore, the GCF of 3410/472,4205/964 is 5/113752.
To find the highest common factor of 3410,4205, we have to find the factors of both numbers and list the highest common factor.
The factors of 3410 are 1, 2, 5, 10, 11, 22, 31, 55, 62, 110, 155, 310, 341, 682, 1705, 3410
The factors of 4205 are 1, 5, 29, 145, 841, 4205
The HCF of 3410,4205 is 5.
Lets's calculate GCF of 3410,4205
| 5 | 3410, 4205 |
| 682, 841 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 3410,4205 By Matching Biggest Common Factor Method
Now, list down the factors of 3410
:1,2,5,10,11,22,31,55,62,110,155,310,341,682,1705,3410
Now, list down the factors of 4205
:1,5,29,145,841,4205
Greatest Common Factor
We found the factors 3410,4205 . The biggest common factor number is the GCF number.
So the greatest common factor 3410,4205 is 5.
Lets's calculate LCM of 472,964
| 2 | 472, 964 |
| 2 | 236, 482 |
| 118, 241 |
∴ So the LCM of the given numbers is 2 x 2 x 118 x 241 = 113752
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/113752
Therefore, the GCF of Fractions 3410/472,4205/964 is 5/113752
Least Common Multiple of 472,964 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 472,964 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(472,964) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(472,964) x common factors =4 x 1 = 4
LCM(472,964) = ( 472 × 964 ) / 4
LCM(472,964) = 455008 / 4
LCM(472,964) = 113752
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FAQs on GCF of Fractions of 3410/472, 4205/964
1. What is the HCF of 3410,4205?
The HCF of 3410,4205 is 5
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 3410/472, 4205/964?
Answer: GCF of Numerators as per given numbers 3410/472, 4205/964 is
GCF of Numerators i.e. for 3410,4205 is 5
LCM of denominators i.e. for 472,964 is 113752.
Thus, GCF of Fractions is 5/113752.Finally, GCF of Fractions for 3410/472, 4205/964 is 5/113752.