GCF of 4123/498, 9207/714
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4123/498, 9207/714 i.e 31/59262 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4123/498, 9207/714.
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 4123/498,9207/714?
Given fractions are 4123/498,9207/714
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 4123/498,9207/714, numerators are 4123,9207
Denominators are 498,714
The GCF of 4123,9207 is 31 .
LCM of 498,714 is 59262.
The greatest common factor of 4123/498,9207/714 = [GCF of 4123,9207]/[LCM of 498,714]= 31/59262
Therefore, the GCF of 4123/498,9207/714 is 31/59262.
To find the highest common factor of 4123,9207, we have to find the factors of both numbers and list the highest common factor.
The factors of 4123 are 1, 7, 19, 31, 133, 217, 589, 4123
The factors of 9207 are 1, 3, 9, 11, 27, 31, 33, 93, 99, 279, 297, 341, 837, 1023, 3069, 9207
The HCF of 4123,9207 is 31.
Lets's calculate GCF of 4123,9207
| 31 | 4123, 9207 |
| 133, 297 |
∴ So the GCF of the given numbers is 31 = 31
Greatest Common Factor of 4123,9207 By Matching Biggest Common Factor Method
Now, list down the factors of 4123
:1,7,19,31,133,217,589,4123
Now, list down the factors of 9207
:1,3,9,11,27,31,33,93,99,279,297,341,837,1023,3069,9207
Greatest Common Factor
We found the factors 4123,9207 . The biggest common factor number is the GCF number.
So the greatest common factor 4123,9207 is 31.
Lets's calculate LCM of 498,714
| 2 | 498, 714 |
| 3 | 249, 357 |
| 83, 119 |
∴ So the LCM of the given numbers is 2 x 3 x 83 x 119 = 59262
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/59262
Therefore, the GCF of Fractions 4123/498,9207/714 is 31/59262
Least Common Multiple of 498,714 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 498,714 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(498,714) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(498,714) x common factors =6 x 1 = 6
LCM(498,714) = ( 498 × 714 ) / 6
LCM(498,714) = 355572 / 6
LCM(498,714) = 59262
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FAQs on GCF of Fractions of 4123/498, 9207/714
1. What is the HCF of 4123,9207?
The HCF of 4123,9207 is 31
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 4123/498, 9207/714?
Answer: GCF of Numerators as per given numbers 4123/498, 9207/714 is
GCF of Numerators i.e. for 4123,9207 is 31
LCM of denominators i.e. for 498,714 is 59262.
Thus, GCF of Fractions is 31/59262.Finally, GCF of Fractions for 4123/498, 9207/714 is 31/59262.