GCF of 5724/340, 3528/1207
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5724/340, 3528/1207 i.e 36/24140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5724/340, 3528/1207.
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 5724/340,3528/1207?
Given fractions are 5724/340,3528/1207
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 5724/340,3528/1207, numerators are 5724,3528
Denominators are 340,1207
The GCF of 5724,3528 is 36 .
LCM of 340,1207 is 24140.
The greatest common factor of 5724/340,3528/1207 = [GCF of 5724,3528]/[LCM of 340,1207]= 36/24140
Therefore, the GCF of 5724/340,3528/1207 is 36/24140.
To find the highest common factor of 5724,3528, we have to find the factors of both numbers and list the highest common factor.
The factors of 5724 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 53, 54, 106, 108, 159, 212, 318, 477, 636, 954, 1431, 1908, 2862, 5724
The factors of 3528 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 49, 56, 63, 72, 84, 98, 126, 147, 168, 196, 252, 294, 392, 441, 504, 588, 882, 1176, 1764, 3528
The HCF of 5724,3528 is 36.
Lets's calculate GCF of 5724,3528
| 2 | 5724, 3528 |
| 2 | 2862, 1764 |
| 3 | 1431, 882 |
| 3 | 477, 294 |
| 159, 98 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 3 = 36
Greatest Common Factor of 5724,3528 By Matching Biggest Common Factor Method
Now, list down the factors of 5724
:1,2,3,4,6,9,12,18,27,36,53,54,106,108,159,212,318,477,636,954,1431,1908,2862,5724
Now, list down the factors of 3528
:1,2,3,4,6,7,8,9,12,14,18,21,24,28,36,42,49,56,63,72,84,98,126,147,168,196,252,294,392,441,504,588,882,1176,1764,3528
Greatest Common Factor
We found the factors 5724,3528 . The biggest common factor number is the GCF number.
So the greatest common factor 5724,3528 is 36.
Lets's calculate LCM of 340,1207
| 17 | 340, 1207 |
| 20, 71 |
∴ So the LCM of the given numbers is 17 x 20 x 71 = 24140
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 36/24140
Therefore, the GCF of Fractions 5724/340,3528/1207 is 36/24140
Least Common Multiple of 340,1207 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 340,1207 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(340,1207) = 17
common factors(in case of two or more numbers have common factors) = 1
GCF(340,1207) x common factors =17 x 1 = 17
LCM(340,1207) = ( 340 × 1207 ) / 17
LCM(340,1207) = 410380 / 17
LCM(340,1207) = 24140
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 5724/340, 3528/1207
1. What is the HCF of 5724,3528?
The HCF of 5724,3528 is 36
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 5724/340, 3528/1207?
Answer: GCF of Numerators as per given numbers 5724/340, 3528/1207 is
GCF of Numerators i.e. for 5724,3528 is 36
LCM of denominators i.e. for 340,1207 is 24140.
Thus, GCF of Fractions is 36/24140.Finally, GCF of Fractions for 5724/340, 3528/1207 is 36/24140.