GCF of 216/17, 596/101
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 216/17, 596/101 i.e 4/1717 easily. The following is the detailed procedure to determine the greatest common factor of fractions 216/17, 596/101.
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 216/17,596/101?
Given fractions are 216/17,596/101
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 216/17,596/101, numerators are 216,596
Denominators are 17,101
The GCF of 216,596 is 4 .
LCM of 17,101 is 1717.
The greatest common factor of 216/17,596/101 = [GCF of 216,596]/[LCM of 17,101]= 4/1717
Therefore, the GCF of 216/17,596/101 is 4/1717.
To find the highest common factor of 216,596, we have to find the factors of both numbers and list the highest common factor.
The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
The factors of 596 are 1, 2, 4, 149, 298, 596
The HCF of 216,596 is 4.
Lets's calculate GCF of 216,596
| 2 | 216, 596 |
| 2 | 108, 298 |
| 54, 149 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 216,596 By Matching Biggest Common Factor Method
Now, list down the factors of 216
:1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216
Now, list down the factors of 596
:1,2,4,149,298,596
Greatest Common Factor
We found the factors 216,596 . The biggest common factor number is the GCF number.
So the greatest common factor 216,596 is 4.
Lets's calculate LCM of 17,101
Given numbers has no common factors except 1. So, there LCM is their product i.e 1717
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/1717
Therefore, the GCF of Fractions 216/17,596/101 is 4/1717
Least Common Multiple of 17,101 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 17,101 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(17,101) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(17,101) x common factors =1 x 1 = 1
LCM(17,101) = ( 17 × 101 ) / 1
LCM(17,101) = 1717 / 1
LCM(17,101) = 1717
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 216/17, 596/101
1. What is the HCF of 216,596?
The HCF of 216,596 is 4
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 216/17, 596/101?
Answer: GCF of Numerators as per given numbers 216/17, 596/101 is
GCF of Numerators i.e. for 216,596 is 4
LCM of denominators i.e. for 17,101 is 1717.
Thus, GCF of Fractions is 4/1717.Finally, GCF of Fractions for 216/17, 596/101 is 4/1717.