GCF of 9114/354, 5205/7206
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9114/354, 5205/7206 i.e 3/425154 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9114/354, 5205/7206.
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 9114/354,5205/7206?
Given fractions are 9114/354,5205/7206
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 9114/354,5205/7206, numerators are 9114,5205
Denominators are 354,7206
The GCF of 9114,5205 is 3 .
LCM of 354,7206 is 425154.
The greatest common factor of 9114/354,5205/7206 = [GCF of 9114,5205]/[LCM of 354,7206]= 3/425154
Therefore, the GCF of 9114/354,5205/7206 is 3/425154.
To find the highest common factor of 9114,5205, we have to find the factors of both numbers and list the highest common factor.
The factors of 9114 are 1, 2, 3, 6, 7, 14, 21, 31, 42, 49, 62, 93, 98, 147, 186, 217, 294, 434, 651, 1302, 1519, 3038, 4557, 9114
The factors of 5205 are 1, 3, 5, 15, 347, 1041, 1735, 5205
The HCF of 9114,5205 is 3.
Lets's calculate GCF of 9114,5205
| 3 | 9114, 5205 |
| 3038, 1735 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 9114,5205 By Matching Biggest Common Factor Method
Now, list down the factors of 9114
:1,2,3,6,7,14,21,31,42,49,62,93,98,147,186,217,294,434,651,1302,1519,3038,4557,9114
Now, list down the factors of 5205
:1,3,5,15,347,1041,1735,5205
Greatest Common Factor
We found the factors 9114,5205 . The biggest common factor number is the GCF number.
So the greatest common factor 9114,5205 is 3.
Lets's calculate LCM of 354,7206
| 2 | 354, 7206 |
| 3 | 177, 3603 |
| 59, 1201 |
∴ So the LCM of the given numbers is 2 x 3 x 59 x 1201 = 425154
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/425154
Therefore, the GCF of Fractions 9114/354,5205/7206 is 3/425154
Least Common Multiple of 354,7206 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 354,7206 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(354,7206) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(354,7206) x common factors =6 x 1 = 6
LCM(354,7206) = ( 354 × 7206 ) / 6
LCM(354,7206) = 2550924 / 6
LCM(354,7206) = 425154
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FAQs on GCF of Fractions of 9114/354, 5205/7206
1. What is the HCF of 9114,5205?
The HCF of 9114,5205 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 9114/354, 5205/7206?
Answer: GCF of Numerators as per given numbers 9114/354, 5205/7206 is
GCF of Numerators i.e. for 9114,5205 is 3
LCM of denominators i.e. for 354,7206 is 425154.
Thus, GCF of Fractions is 3/425154.Finally, GCF of Fractions for 9114/354, 5205/7206 is 3/425154.