GCF of 537/748, 1209/170
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 537/748, 1209/170 i.e 3/3740 easily. The following is the detailed procedure to determine the greatest common factor of fractions 537/748, 1209/170.
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 537/748,1209/170?
Given fractions are 537/748,1209/170
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 537/748,1209/170, numerators are 537,1209
Denominators are 748,170
The GCF of 537,1209 is 3 .
LCM of 748,170 is 3740.
The greatest common factor of 537/748,1209/170 = [GCF of 537,1209]/[LCM of 748,170]= 3/3740
Therefore, the GCF of 537/748,1209/170 is 3/3740.
To find the highest common factor of 537,1209, we have to find the factors of both numbers and list the highest common factor.
The factors of 537 are 1, 3, 179, 537
The factors of 1209 are 1, 3, 13, 31, 39, 93, 403, 1209
The HCF of 537,1209 is 3.
Lets's calculate GCF of 537,1209
| 3 | 537, 1209 |
| 179, 403 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 537,1209 By Matching Biggest Common Factor Method
Now, list down the factors of 537
:1,3,179,537
Now, list down the factors of 1209
:1,3,13,31,39,93,403,1209
Greatest Common Factor
We found the factors 537,1209 . The biggest common factor number is the GCF number.
So the greatest common factor 537,1209 is 3.
Lets's calculate LCM of 748,170
| 2 | 748, 170 |
| 17 | 374, 85 |
| 22, 5 |
∴ So the LCM of the given numbers is 2 x 17 x 22 x 5 = 3740
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/3740
Therefore, the GCF of Fractions 537/748,1209/170 is 3/3740
Least Common Multiple of 748,170 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 748,170 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(748,170) = 34
common factors(in case of two or more numbers have common factors) = 1
GCF(748,170) x common factors =34 x 1 = 34
LCM(748,170) = ( 748 × 170 ) / 34
LCM(748,170) = 127160 / 34
LCM(748,170) = 3740
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FAQs on GCF of Fractions of 537/748, 1209/170
1. What is the HCF of 537,1209?
The HCF of 537,1209 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 537/748, 1209/170?
Answer: GCF of Numerators as per given numbers 537/748, 1209/170 is
GCF of Numerators i.e. for 537,1209 is 3
LCM of denominators i.e. for 748,170 is 3740.
Thus, GCF of Fractions is 3/3740.Finally, GCF of Fractions for 537/748, 1209/170 is 3/3740.