GCF of 48/39, 71/21, 213/402
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 48/39, 71/21, 213/402 i.e 1/36582 easily. The following is the detailed procedure to determine the greatest common factor of fractions 48/39, 71/21, 213/402.
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 48/39,71/21,213/402?
Given fractions are 48/39,71/21,213/402
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 48/39,71/21,213/402, numerators are 48,71,213
Denominators are 39,21,402
The GCF of 48,71,213 is 1 .
LCM of 39,21,402 is 36582.
The greatest common factor of 48/39,71/21,213/402 = [GCF of 48,71,213]/[LCM of 39,21,402]= 1/36582
Therefore, the GCF of 48/39,71/21,213/402 is 1/36582.
To find the highest common factor of 48,71,213, we have to find the factors of both numbers and list the highest common factor.
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 71 are 1, 71
The factors of 213 are 1, 3, 71, 213
The HCF of 48,71,213 is 1.
Lets's calculate GCF of 48,71,213
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 48,71,213 By Matching Biggest Common Factor Method
Now, list down the factors of 48
:1,2,3,4,6,8,12,16,24,48
Now, list down the factors of 71
:1,71
Now, list down the factors of 213
:1,3,71,213
Greatest Common Factor
We found the factors 48,71,213 . The biggest common factor number is the GCF number.
So the greatest common factor 48,71,213 is 1.
Lets's calculate LCM of 39,21,402
| 3 | 39, 21, 402 |
| 13, 7, 134 |
∴ So the LCM of the given numbers is 3 x 13 x 7 x 134 = 36582
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/36582
Therefore, the GCF of Fractions 48/39,71/21,213/402 is 1/36582
Least Common Multiple of 39,21,402 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 39,21,402 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(39,21,402) = 3
common factors(in case of two or more numbers have common factors) = 3
GCF(39,21,402) x common factors =3 x 3 = 9
LCM(39,21,402) = ( 39 × 21 × 402 ) / 9
LCM(39,21,402) = 329238 / 9
LCM(39,21,402) = 36582
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FAQs on GCF of Fractions of 48/39, 71/21, 213/402
1. What is the HCF of 48,71,213?
The HCF of 48,71,213 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 48/39, 71/21, 213/402?
Answer: GCF of Numerators as per given numbers 48/39, 71/21, 213/402 is
GCF of Numerators i.e. for 48,71,213 is 1
LCM of denominators i.e. for 39,21,402 is 36582.
Thus, GCF of Fractions is 1/36582.Finally, GCF of Fractions for 48/39, 71/21, 213/402 is 1/36582.