GCF of 1745/354, 1416/4125
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1745/354, 1416/4125 i.e 1/486750 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1745/354, 1416/4125.
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 1745/354,1416/4125?
Given fractions are 1745/354,1416/4125
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 1745/354,1416/4125, numerators are 1745,1416
Denominators are 354,4125
The GCF of 1745,1416 is 1 .
LCM of 354,4125 is 486750.
The greatest common factor of 1745/354,1416/4125 = [GCF of 1745,1416]/[LCM of 354,4125]= 1/486750
Therefore, the GCF of 1745/354,1416/4125 is 1/486750.
To find the highest common factor of 1745,1416, we have to find the factors of both numbers and list the highest common factor.
The factors of 1745 are 1, 5, 349, 1745
The factors of 1416 are 1, 2, 3, 4, 6, 8, 12, 24, 59, 118, 177, 236, 354, 472, 708, 1416
The HCF of 1745,1416 is 1.
Lets's calculate GCF of 1745,1416
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 1745,1416 By Matching Biggest Common Factor Method
Now, list down the factors of 1745
:1,5,349,1745
Now, list down the factors of 1416
:1,2,3,4,6,8,12,24,59,118,177,236,354,472,708,1416
Greatest Common Factor
We found the factors 1745,1416 . The biggest common factor number is the GCF number.
So the greatest common factor 1745,1416 is 1.
Lets's calculate LCM of 354,4125
| 3 | 354, 4125 |
| 118, 1375 |
∴ So the LCM of the given numbers is 3 x 118 x 1375 = 486750
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/486750
Therefore, the GCF of Fractions 1745/354,1416/4125 is 1/486750
Least Common Multiple of 354,4125 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 354,4125 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(354,4125) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(354,4125) x common factors =3 x 1 = 3
LCM(354,4125) = ( 354 × 4125 ) / 3
LCM(354,4125) = 1460250 / 3
LCM(354,4125) = 486750
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FAQs on GCF of Fractions of 1745/354, 1416/4125
1. What is the HCF of 1745,1416?
The HCF of 1745,1416 is 1
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 1745/354, 1416/4125?
Answer: GCF of Numerators as per given numbers 1745/354, 1416/4125 is
GCF of Numerators i.e. for 1745,1416 is 1
LCM of denominators i.e. for 354,4125 is 486750.
Thus, GCF of Fractions is 1/486750.Finally, GCF of Fractions for 1745/354, 1416/4125 is 1/486750.