GCF of 525/49, 300/209
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 525/49, 300/209 i.e 75/10241 easily. The following is the detailed procedure to determine the greatest common factor of fractions 525/49, 300/209.
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 525/49,300/209?
Given fractions are 525/49,300/209
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 525/49,300/209, numerators are 525,300
Denominators are 49,209
The GCF of 525,300 is 75 .
LCM of 49,209 is 10241.
The greatest common factor of 525/49,300/209 = [GCF of 525,300]/[LCM of 49,209]= 75/10241
Therefore, the GCF of 525/49,300/209 is 75/10241.
To find the highest common factor of 525,300, we have to find the factors of both numbers and list the highest common factor.
The factors of 525 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, 525
The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
The HCF of 525,300 is 75.
Lets's calculate GCF of 525,300
| 3 | 525, 300 |
| 5 | 175, 100 |
| 5 | 35, 20 |
| 7, 4 |
∴ So the GCF of the given numbers is 3 x 5 x 5 = 75
Greatest Common Factor of 525,300 By Matching Biggest Common Factor Method
Now, list down the factors of 525
:1,3,5,7,15,21,25,35,75,105,175,525
Now, list down the factors of 300
:1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300
Greatest Common Factor
We found the factors 525,300 . The biggest common factor number is the GCF number.
So the greatest common factor 525,300 is 75.
Lets's calculate LCM of 49,209
Given numbers has no common factors except 1. So, there LCM is their product i.e 10241
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 75/10241
Therefore, the GCF of Fractions 525/49,300/209 is 75/10241
Least Common Multiple of 49,209 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 49,209 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(49,209) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(49,209) x common factors =1 x 1 = 1
LCM(49,209) = ( 49 × 209 ) / 1
LCM(49,209) = 10241 / 1
LCM(49,209) = 10241
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FAQs on GCF of Fractions of 525/49, 300/209
1. What is the HCF of 525,300?
The HCF of 525,300 is 75
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 525/49, 300/209?
Answer: GCF of Numerators as per given numbers 525/49, 300/209 is
GCF of Numerators i.e. for 525,300 is 75
LCM of denominators i.e. for 49,209 is 10241.
Thus, GCF of Fractions is 75/10241.Finally, GCF of Fractions for 525/49, 300/209 is 75/10241.