GCF of 65/106, 412/442, 217/177
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 65/106, 412/442, 217/177 i.e 1/4146402 easily. The following is the detailed procedure to determine the greatest common factor of fractions 65/106, 412/442, 217/177.
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 65/106,412/442,217/177?
Given fractions are 65/106,412/442,217/177
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 65/106,412/442,217/177, numerators are 65,412,217
Denominators are 106,442,177
The GCF of 65,412,217 is 1 .
LCM of 106,442,177 is 4146402.
The greatest common factor of 65/106,412/442,217/177 = [GCF of 65,412,217]/[LCM of 106,442,177]= 1/4146402
Therefore, the GCF of 65/106,412/442,217/177 is 1/4146402.
To find the highest common factor of 65,412,217, we have to find the factors of both numbers and list the highest common factor.
The factors of 65 are 1, 5, 13, 65
The factors of 412 are 1, 2, 4, 103, 206, 412
The factors of 217 are 1, 7, 31, 217
The HCF of 65,412,217 is 1.
Lets's calculate GCF of 65,412,217
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 65,412,217 By Matching Biggest Common Factor Method
Now, list down the factors of 65
:1,5,13,65
Now, list down the factors of 412
:1,2,4,103,206,412
Now, list down the factors of 217
:1,7,31,217
Greatest Common Factor
We found the factors 65,412,217 . The biggest common factor number is the GCF number.
So the greatest common factor 65,412,217 is 1.
Lets's calculate LCM of 106,442,177
| 2 | 106, 442, 177 |
| 53, 221, 177 |
∴ So the LCM of the given numbers is 2 x 53 x 221 x 177 = 4146402
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4146402
Therefore, the GCF of Fractions 65/106,412/442,217/177 is 1/4146402
Least Common Multiple of 106,442,177 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 106,442,177 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(106,442,177) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(106,442,177) x common factors =1 x 2 = 2
LCM(106,442,177) = ( 106 × 442 × 177 ) / 2
LCM(106,442,177) = 8292804 / 2
LCM(106,442,177) = 4146402
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FAQs on GCF of Fractions of 65/106, 412/442, 217/177
1. What is the HCF of 65,412,217?
The HCF of 65,412,217 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 65/106, 412/442, 217/177?
Answer: GCF of Numerators as per given numbers 65/106, 412/442, 217/177 is
GCF of Numerators i.e. for 65,412,217 is 1
LCM of denominators i.e. for 106,442,177 is 4146402.
Thus, GCF of Fractions is 1/4146402.Finally, GCF of Fractions for 65/106, 412/442, 217/177 is 1/4146402.