GCF of 1689/364, 1236/362
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1689/364, 1236/362 i.e 3/65884 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1689/364, 1236/362.
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 1689/364,1236/362?
Given fractions are 1689/364,1236/362
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 1689/364,1236/362, numerators are 1689,1236
Denominators are 364,362
The GCF of 1689,1236 is 3 .
LCM of 364,362 is 65884.
The greatest common factor of 1689/364,1236/362 = [GCF of 1689,1236]/[LCM of 364,362]= 3/65884
Therefore, the GCF of 1689/364,1236/362 is 3/65884.
To find the highest common factor of 1689,1236, we have to find the factors of both numbers and list the highest common factor.
The factors of 1689 are 1, 3, 563, 1689
The factors of 1236 are 1, 2, 3, 4, 6, 12, 103, 206, 309, 412, 618, 1236
The HCF of 1689,1236 is 3.
Lets's calculate GCF of 1689,1236
| 3 | 1689, 1236 |
| 563, 412 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 1689,1236 By Matching Biggest Common Factor Method
Now, list down the factors of 1689
:1,3,563,1689
Now, list down the factors of 1236
:1,2,3,4,6,12,103,206,309,412,618,1236
Greatest Common Factor
We found the factors 1689,1236 . The biggest common factor number is the GCF number.
So the greatest common factor 1689,1236 is 3.
Lets's calculate LCM of 364,362
| 2 | 364, 362 |
| 182, 181 |
∴ So the LCM of the given numbers is 2 x 182 x 181 = 65884
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/65884
Therefore, the GCF of Fractions 1689/364,1236/362 is 3/65884
Least Common Multiple of 364,362 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 364,362 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(364,362) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(364,362) x common factors =2 x 1 = 2
LCM(364,362) = ( 364 × 362 ) / 2
LCM(364,362) = 131768 / 2
LCM(364,362) = 65884
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FAQs on GCF of Fractions of 1689/364, 1236/362
1. What is the HCF of 1689,1236?
The HCF of 1689,1236 is 3
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 1689/364, 1236/362?
Answer: GCF of Numerators as per given numbers 1689/364, 1236/362 is
GCF of Numerators i.e. for 1689,1236 is 3
LCM of denominators i.e. for 364,362 is 65884.
Thus, GCF of Fractions is 3/65884.Finally, GCF of Fractions for 1689/364, 1236/362 is 3/65884.