GCF of 7231/814, 3213/7500
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7231/814, 3213/7500 i.e 7/3052500 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7231/814, 3213/7500.
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 7231/814,3213/7500?
Given fractions are 7231/814,3213/7500
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 7231/814,3213/7500, numerators are 7231,3213
Denominators are 814,7500
The GCF of 7231,3213 is 7 .
LCM of 814,7500 is 3052500.
The greatest common factor of 7231/814,3213/7500 = [GCF of 7231,3213]/[LCM of 814,7500]= 7/3052500
Therefore, the GCF of 7231/814,3213/7500 is 7/3052500.
To find the highest common factor of 7231,3213, we have to find the factors of both numbers and list the highest common factor.
The factors of 7231 are 1, 7, 1033, 7231
The factors of 3213 are 1, 3, 7, 9, 17, 21, 27, 51, 63, 119, 153, 189, 357, 459, 1071, 3213
The HCF of 7231,3213 is 7.
Lets's calculate GCF of 7231,3213
| 7 | 7231, 3213 |
| 1033, 459 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 7231,3213 By Matching Biggest Common Factor Method
Now, list down the factors of 7231
:1,7,1033,7231
Now, list down the factors of 3213
:1,3,7,9,17,21,27,51,63,119,153,189,357,459,1071,3213
Greatest Common Factor
We found the factors 7231,3213 . The biggest common factor number is the GCF number.
So the greatest common factor 7231,3213 is 7.
Lets's calculate LCM of 814,7500
| 2 | 814, 7500 |
| 407, 3750 |
∴ So the LCM of the given numbers is 2 x 407 x 3750 = 3052500
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/3052500
Therefore, the GCF of Fractions 7231/814,3213/7500 is 7/3052500
Least Common Multiple of 814,7500 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 814,7500 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(814,7500) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(814,7500) x common factors =2 x 1 = 2
LCM(814,7500) = ( 814 × 7500 ) / 2
LCM(814,7500) = 6105000 / 2
LCM(814,7500) = 3052500
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FAQs on GCF of Fractions of 7231/814, 3213/7500
1. What is the HCF of 7231,3213?
The HCF of 7231,3213 is 7
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 7231/814, 3213/7500?
Answer: GCF of Numerators as per given numbers 7231/814, 3213/7500 is
GCF of Numerators i.e. for 7231,3213 is 7
LCM of denominators i.e. for 814,7500 is 3052500.
Thus, GCF of Fractions is 7/3052500.Finally, GCF of Fractions for 7231/814, 3213/7500 is 7/3052500.