GCF of 689/703, 1908/209
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 689/703, 1908/209 i.e 53/7733 easily. The following is the detailed procedure to determine the greatest common factor of fractions 689/703, 1908/209.
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 689/703,1908/209?
Given fractions are 689/703,1908/209
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 689/703,1908/209, numerators are 689,1908
Denominators are 703,209
The GCF of 689,1908 is 53 .
LCM of 703,209 is 7733.
The greatest common factor of 689/703,1908/209 = [GCF of 689,1908]/[LCM of 703,209]= 53/7733
Therefore, the GCF of 689/703,1908/209 is 53/7733.
To find the highest common factor of 689,1908, we have to find the factors of both numbers and list the highest common factor.
The factors of 689 are 1, 13, 53, 689
The factors of 1908 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 53, 106, 159, 212, 318, 477, 636, 954, 1908
The HCF of 689,1908 is 53.
Lets's calculate GCF of 689,1908
| 53 | 689, 1908 |
| 13, 36 |
∴ So the GCF of the given numbers is 53 = 53
Greatest Common Factor of 689,1908 By Matching Biggest Common Factor Method
Now, list down the factors of 689
:1,13,53,689
Now, list down the factors of 1908
:1,2,3,4,6,9,12,18,36,53,106,159,212,318,477,636,954,1908
Greatest Common Factor
We found the factors 689,1908 . The biggest common factor number is the GCF number.
So the greatest common factor 689,1908 is 53.
Lets's calculate LCM of 703,209
| 19 | 703, 209 |
| 37, 11 |
∴ So the LCM of the given numbers is 19 x 37 x 11 = 7733
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 53/7733
Therefore, the GCF of Fractions 689/703,1908/209 is 53/7733
Least Common Multiple of 703,209 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 703,209 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(703,209) = 19
common factors(in case of two or more numbers have common factors) = 1
GCF(703,209) x common factors =19 x 1 = 19
LCM(703,209) = ( 703 × 209 ) / 19
LCM(703,209) = 146927 / 19
LCM(703,209) = 7733
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 689/703, 1908/209
1. What is the HCF of 689,1908?
The HCF of 689,1908 is 53
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 689/703, 1908/209?
Answer: GCF of Numerators as per given numbers 689/703, 1908/209 is
GCF of Numerators i.e. for 689,1908 is 53
LCM of denominators i.e. for 703,209 is 7733.
Thus, GCF of Fractions is 53/7733.Finally, GCF of Fractions for 689/703, 1908/209 is 53/7733.