GCF of 1596/516, 9709/5724
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1596/516, 9709/5724 i.e 133/246132 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1596/516, 9709/5724.
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 1596/516,9709/5724?
Given fractions are 1596/516,9709/5724
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 1596/516,9709/5724, numerators are 1596,9709
Denominators are 516,5724
The GCF of 1596,9709 is 133 .
LCM of 516,5724 is 246132.
The greatest common factor of 1596/516,9709/5724 = [GCF of 1596,9709]/[LCM of 516,5724]= 133/246132
Therefore, the GCF of 1596/516,9709/5724 is 133/246132.
To find the highest common factor of 1596,9709, we have to find the factors of both numbers and list the highest common factor.
The factors of 1596 are 1, 2, 3, 4, 6, 7, 12, 14, 19, 21, 28, 38, 42, 57, 76, 84, 114, 133, 228, 266, 399, 532, 798, 1596
The factors of 9709 are 1, 7, 19, 73, 133, 511, 1387, 9709
The HCF of 1596,9709 is 133.
Lets's calculate GCF of 1596,9709
| 7 | 1596, 9709 |
| 19 | 228, 1387 |
| 12, 73 |
∴ So the GCF of the given numbers is 7 x 19 = 133
Greatest Common Factor of 1596,9709 By Matching Biggest Common Factor Method
Now, list down the factors of 1596
:1,2,3,4,6,7,12,14,19,21,28,38,42,57,76,84,114,133,228,266,399,532,798,1596
Now, list down the factors of 9709
:1,7,19,73,133,511,1387,9709
Greatest Common Factor
We found the factors 1596,9709 . The biggest common factor number is the GCF number.
So the greatest common factor 1596,9709 is 133.
Lets's calculate LCM of 516,5724
| 2 | 516, 5724 |
| 2 | 258, 2862 |
| 3 | 129, 1431 |
| 43, 477 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 43 x 477 = 246132
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 133/246132
Therefore, the GCF of Fractions 1596/516,9709/5724 is 133/246132
Least Common Multiple of 516,5724 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 516,5724 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(516,5724) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(516,5724) x common factors =12 x 1 = 12
LCM(516,5724) = ( 516 × 5724 ) / 12
LCM(516,5724) = 2953584 / 12
LCM(516,5724) = 246132
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 1596/516, 9709/5724
1. What is the HCF of 1596,9709?
The HCF of 1596,9709 is 133
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 1596/516, 9709/5724?
Answer: GCF of Numerators as per given numbers 1596/516, 9709/5724 is
GCF of Numerators i.e. for 1596,9709 is 133
LCM of denominators i.e. for 516,5724 is 246132.
Thus, GCF of Fractions is 133/246132.Finally, GCF of Fractions for 1596/516, 9709/5724 is 133/246132.