GCF of 525/60, 828/66, 123/61
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 525/60, 828/66, 123/61 i.e 3/40260 easily. The following is the detailed procedure to determine the greatest common factor of fractions 525/60, 828/66, 123/61.
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 525/60,828/66,123/61?
Given fractions are 525/60,828/66,123/61
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 525/60,828/66,123/61, numerators are 525,828,123
Denominators are 60,66,61
The GCF of 525,828,123 is 3 .
LCM of 60,66,61 is 40260.
The greatest common factor of 525/60,828/66,123/61 = [GCF of 525,828,123]/[LCM of 60,66,61]= 3/40260
Therefore, the GCF of 525/60,828/66,123/61 is 3/40260.
To find the highest common factor of 525,828,123, 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 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828
The factors of 123 are 1, 3, 41, 123
The HCF of 525,828,123 is 3.
Lets's calculate GCF of 525,828,123
| 3 | 525, 828, 123 |
| 175, 276, 41 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 525,828,123 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 828
:1,2,3,4,6,9,12,18,23,36,46,69,92,138,207,276,414,828
Now, list down the factors of 123
:1,3,41,123
Greatest Common Factor
We found the factors 525,828,123 . The biggest common factor number is the GCF number.
So the greatest common factor 525,828,123 is 3.
Lets's calculate LCM of 60,66,61
| 2 | 60, 66, 61 |
| 3 | 30, 33, 61 |
| 10, 11, 61 |
∴ So the LCM of the given numbers is 2 x 3 x 10 x 11 x 61 = 40260
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/40260
Therefore, the GCF of Fractions 525/60,828/66,123/61 is 3/40260
Least Common Multiple of 60,66,61 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 60,66,61 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(60,66,61) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(60,66,61) x common factors =1 x 6 = 6
LCM(60,66,61) = ( 60 × 66 × 61 ) / 6
LCM(60,66,61) = 241560 / 6
LCM(60,66,61) = 40260
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 525/60, 828/66, 123/61
1. What is the HCF of 525,828,123?
The HCF of 525,828,123 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 525/60, 828/66, 123/61?
Answer: GCF of Numerators as per given numbers 525/60, 828/66, 123/61 is
GCF of Numerators i.e. for 525,828,123 is 3
LCM of denominators i.e. for 60,66,61 is 40260.
Thus, GCF of Fractions is 3/40260.Finally, GCF of Fractions for 525/60, 828/66, 123/61 is 3/40260.