GCF of 3522/408, 1752/1724
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3522/408, 1752/1724 i.e 6/175848 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3522/408, 1752/1724.
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 3522/408,1752/1724?
Given fractions are 3522/408,1752/1724
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 3522/408,1752/1724, numerators are 3522,1752
Denominators are 408,1724
The GCF of 3522,1752 is 6 .
LCM of 408,1724 is 175848.
The greatest common factor of 3522/408,1752/1724 = [GCF of 3522,1752]/[LCM of 408,1724]= 6/175848
Therefore, the GCF of 3522/408,1752/1724 is 6/175848.
To find the highest common factor of 3522,1752, we have to find the factors of both numbers and list the highest common factor.
The factors of 3522 are 1, 2, 3, 6, 587, 1174, 1761, 3522
The factors of 1752 are 1, 2, 3, 4, 6, 8, 12, 24, 73, 146, 219, 292, 438, 584, 876, 1752
The HCF of 3522,1752 is 6.
Lets's calculate GCF of 3522,1752
| 2 | 3522, 1752 |
| 3 | 1761, 876 |
| 587, 292 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 3522,1752 By Matching Biggest Common Factor Method
Now, list down the factors of 3522
:1,2,3,6,587,1174,1761,3522
Now, list down the factors of 1752
:1,2,3,4,6,8,12,24,73,146,219,292,438,584,876,1752
Greatest Common Factor
We found the factors 3522,1752 . The biggest common factor number is the GCF number.
So the greatest common factor 3522,1752 is 6.
Lets's calculate LCM of 408,1724
| 2 | 408, 1724 |
| 2 | 204, 862 |
| 102, 431 |
∴ So the LCM of the given numbers is 2 x 2 x 102 x 431 = 175848
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/175848
Therefore, the GCF of Fractions 3522/408,1752/1724 is 6/175848
Least Common Multiple of 408,1724 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 408,1724 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(408,1724) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(408,1724) x common factors =4 x 1 = 4
LCM(408,1724) = ( 408 × 1724 ) / 4
LCM(408,1724) = 703392 / 4
LCM(408,1724) = 175848
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FAQs on GCF of Fractions of 3522/408, 1752/1724
1. What is the HCF of 3522,1752?
The HCF of 3522,1752 is 6
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 3522/408, 1752/1724?
Answer: GCF of Numerators as per given numbers 3522/408, 1752/1724 is
GCF of Numerators i.e. for 3522,1752 is 6
LCM of denominators i.e. for 408,1724 is 175848.
Thus, GCF of Fractions is 6/175848.Finally, GCF of Fractions for 3522/408, 1752/1724 is 6/175848.