GCF of 1714/204, 8498/9744
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1714/204, 8498/9744 i.e 2/165648 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1714/204, 8498/9744.
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 1714/204,8498/9744?
Given fractions are 1714/204,8498/9744
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 1714/204,8498/9744, numerators are 1714,8498
Denominators are 204,9744
The GCF of 1714,8498 is 2 .
LCM of 204,9744 is 165648.
The greatest common factor of 1714/204,8498/9744 = [GCF of 1714,8498]/[LCM of 204,9744]= 2/165648
Therefore, the GCF of 1714/204,8498/9744 is 2/165648.
To find the highest common factor of 1714,8498, we have to find the factors of both numbers and list the highest common factor.
The factors of 1714 are 1, 2, 857, 1714
The factors of 8498 are 1, 2, 7, 14, 607, 1214, 4249, 8498
The HCF of 1714,8498 is 2.
Lets's calculate GCF of 1714,8498
| 2 | 1714, 8498 |
| 857, 4249 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1714,8498 By Matching Biggest Common Factor Method
Now, list down the factors of 1714
:1,2,857,1714
Now, list down the factors of 8498
:1,2,7,14,607,1214,4249,8498
Greatest Common Factor
We found the factors 1714,8498 . The biggest common factor number is the GCF number.
So the greatest common factor 1714,8498 is 2.
Lets's calculate LCM of 204,9744
| 2 | 204, 9744 |
| 2 | 102, 4872 |
| 3 | 51, 2436 |
| 17, 812 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 17 x 812 = 165648
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/165648
Therefore, the GCF of Fractions 1714/204,8498/9744 is 2/165648
Least Common Multiple of 204,9744 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 204,9744 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(204,9744) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(204,9744) x common factors =12 x 1 = 12
LCM(204,9744) = ( 204 × 9744 ) / 12
LCM(204,9744) = 1987776 / 12
LCM(204,9744) = 165648
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FAQs on GCF of Fractions of 1714/204, 8498/9744
1. What is the HCF of 1714,8498?
The HCF of 1714,8498 is 2
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 1714/204, 8498/9744?
Answer: GCF of Numerators as per given numbers 1714/204, 8498/9744 is
GCF of Numerators i.e. for 1714,8498 is 2
LCM of denominators i.e. for 204,9744 is 165648.
Thus, GCF of Fractions is 2/165648.Finally, GCF of Fractions for 1714/204, 8498/9744 is 2/165648.