GCF of 7365/416, 5175/7212
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7365/416, 5175/7212 i.e 15/750048 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7365/416, 5175/7212.
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 7365/416,5175/7212?
Given fractions are 7365/416,5175/7212
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 7365/416,5175/7212, numerators are 7365,5175
Denominators are 416,7212
The GCF of 7365,5175 is 15 .
LCM of 416,7212 is 750048.
The greatest common factor of 7365/416,5175/7212 = [GCF of 7365,5175]/[LCM of 416,7212]= 15/750048
Therefore, the GCF of 7365/416,5175/7212 is 15/750048.
To find the highest common factor of 7365,5175, we have to find the factors of both numbers and list the highest common factor.
The factors of 7365 are 1, 3, 5, 15, 491, 1473, 2455, 7365
The factors of 5175 are 1, 3, 5, 9, 15, 23, 25, 45, 69, 75, 115, 207, 225, 345, 575, 1035, 1725, 5175
The HCF of 7365,5175 is 15.
Lets's calculate GCF of 7365,5175
| 3 | 7365, 5175 |
| 5 | 2455, 1725 |
| 491, 345 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 7365,5175 By Matching Biggest Common Factor Method
Now, list down the factors of 7365
:1,3,5,15,491,1473,2455,7365
Now, list down the factors of 5175
:1,3,5,9,15,23,25,45,69,75,115,207,225,345,575,1035,1725,5175
Greatest Common Factor
We found the factors 7365,5175 . The biggest common factor number is the GCF number.
So the greatest common factor 7365,5175 is 15.
Lets's calculate LCM of 416,7212
| 2 | 416, 7212 |
| 2 | 208, 3606 |
| 104, 1803 |
∴ So the LCM of the given numbers is 2 x 2 x 104 x 1803 = 750048
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/750048
Therefore, the GCF of Fractions 7365/416,5175/7212 is 15/750048
Least Common Multiple of 416,7212 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 416,7212 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(416,7212) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(416,7212) x common factors =4 x 1 = 4
LCM(416,7212) = ( 416 × 7212 ) / 4
LCM(416,7212) = 3000192 / 4
LCM(416,7212) = 750048
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FAQs on GCF of Fractions of 7365/416, 5175/7212
1. What is the HCF of 7365,5175?
The HCF of 7365,5175 is 15
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 7365/416, 5175/7212?
Answer: GCF of Numerators as per given numbers 7365/416, 5175/7212 is
GCF of Numerators i.e. for 7365,5175 is 15
LCM of denominators i.e. for 416,7212 is 750048.
Thus, GCF of Fractions is 15/750048.Finally, GCF of Fractions for 7365/416, 5175/7212 is 15/750048.