GCF of 525/32, 210/2356
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 525/32, 210/2356 i.e 105/18848 easily. The following is the detailed procedure to determine the greatest common factor of fractions 525/32, 210/2356.
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 525/32,210/2356?
Given fractions are 525/32,210/2356
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 525/32,210/2356, numerators are 525,210
Denominators are 32,2356
The GCF of 525,210 is 105 .
LCM of 32,2356 is 18848.
The greatest common factor of 525/32,210/2356 = [GCF of 525,210]/[LCM of 32,2356]= 105/18848
Therefore, the GCF of 525/32,210/2356 is 105/18848.
To find the highest common factor of 525,210, 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 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
The HCF of 525,210 is 105.
Lets's calculate GCF of 525,210
| 3 | 525, 210 |
| 5 | 175, 70 |
| 7 | 35, 14 |
| 5, 2 |
∴ So the GCF of the given numbers is 3 x 5 x 7 = 105
Greatest Common Factor of 525,210 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 210
:1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210
Greatest Common Factor
We found the factors 525,210 . The biggest common factor number is the GCF number.
So the greatest common factor 525,210 is 105.
Lets's calculate LCM of 32,2356
| 2 | 32, 2356 |
| 2 | 16, 1178 |
| 8, 589 |
∴ So the LCM of the given numbers is 2 x 2 x 8 x 589 = 18848
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 105/18848
Therefore, the GCF of Fractions 525/32,210/2356 is 105/18848
Least Common Multiple of 32,2356 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 32,2356 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,2356) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(32,2356) x common factors =4 x 1 = 4
LCM(32,2356) = ( 32 × 2356 ) / 4
LCM(32,2356) = 75392 / 4
LCM(32,2356) = 18848
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FAQs on GCF of Fractions of 525/32, 210/2356
1. What is the HCF of 525,210?
The HCF of 525,210 is 105
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 525/32, 210/2356?
Answer: GCF of Numerators as per given numbers 525/32, 210/2356 is
GCF of Numerators i.e. for 525,210 is 105
LCM of denominators i.e. for 32,2356 is 18848.
Thus, GCF of Fractions is 105/18848.Finally, GCF of Fractions for 525/32, 210/2356 is 105/18848.