GCF of 216/289, 836/126
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 216/289, 836/126 i.e 4/36414 easily. The following is the detailed procedure to determine the greatest common factor of fractions 216/289, 836/126.
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 216/289,836/126?
Given fractions are 216/289,836/126
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 216/289,836/126, numerators are 216,836
Denominators are 289,126
The GCF of 216,836 is 4 .
LCM of 289,126 is 36414.
The greatest common factor of 216/289,836/126 = [GCF of 216,836]/[LCM of 289,126]= 4/36414
Therefore, the GCF of 216/289,836/126 is 4/36414.
To find the highest common factor of 216,836, 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 836 are 1, 2, 4, 11, 19, 22, 38, 44, 76, 209, 418, 836
The HCF of 216,836 is 4.
Lets's calculate GCF of 216,836
| 2 | 216, 836 |
| 2 | 108, 418 |
| 54, 209 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 216,836 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 836
:1,2,4,11,19,22,38,44,76,209,418,836
Greatest Common Factor
We found the factors 216,836 . The biggest common factor number is the GCF number.
So the greatest common factor 216,836 is 4.
Lets's calculate LCM of 289,126
Given numbers has no common factors except 1. So, there LCM is their product i.e 36414
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/36414
Therefore, the GCF of Fractions 216/289,836/126 is 4/36414
Least Common Multiple of 289,126 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 289,126 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(289,126) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(289,126) x common factors =1 x 1 = 1
LCM(289,126) = ( 289 × 126 ) / 1
LCM(289,126) = 36414 / 1
LCM(289,126) = 36414
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FAQs on GCF of Fractions of 216/289, 836/126
1. What is the HCF of 216,836?
The HCF of 216,836 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 216/289, 836/126?
Answer: GCF of Numerators as per given numbers 216/289, 836/126 is
GCF of Numerators i.e. for 216,836 is 4
LCM of denominators i.e. for 289,126 is 36414.
Thus, GCF of Fractions is 4/36414.Finally, GCF of Fractions for 216/289, 836/126 is 4/36414.