GCF of 30/36, 363/21, 407/412
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 30/36, 363/21, 407/412 i.e 1/25956 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/36, 363/21, 407/412.
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 30/36,363/21,407/412?
Given fractions are 30/36,363/21,407/412
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 30/36,363/21,407/412, numerators are 30,363,407
Denominators are 36,21,412
The GCF of 30,363,407 is 1 .
LCM of 36,21,412 is 25956.
The greatest common factor of 30/36,363/21,407/412 = [GCF of 30,363,407]/[LCM of 36,21,412]= 1/25956
Therefore, the GCF of 30/36,363/21,407/412 is 1/25956.
To find the highest common factor of 30,363,407, we have to find the factors of both numbers and list the highest common factor.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 363 are 1, 3, 11, 33, 121, 363
The factors of 407 are 1, 11, 37, 407
The HCF of 30,363,407 is 1.
Lets's calculate GCF of 30,363,407
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 30,363,407 By Matching Biggest Common Factor Method
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 363
:1,3,11,33,121,363
Now, list down the factors of 407
:1,11,37,407
Greatest Common Factor
We found the factors 30,363,407 . The biggest common factor number is the GCF number.
So the greatest common factor 30,363,407 is 1.
Lets's calculate LCM of 36,21,412
| 2 | 36, 21, 412 |
| 2 | 18, 21, 206 |
| 3 | 9, 21, 103 |
| 3, 7, 103 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 7 x 103 = 25956
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/25956
Therefore, the GCF of Fractions 30/36,363/21,407/412 is 1/25956
Least Common Multiple of 36,21,412 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 36,21,412 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(36,21,412) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(36,21,412) x common factors =1 x 12 = 12
LCM(36,21,412) = ( 36 × 21 × 412 ) / 12
LCM(36,21,412) = 311472 / 12
LCM(36,21,412) = 25956
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FAQs on GCF of Fractions of 30/36, 363/21, 407/412
1. What is the HCF of 30,363,407?
The HCF of 30,363,407 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 30/36, 363/21, 407/412?
Answer: GCF of Numerators as per given numbers 30/36, 363/21, 407/412 is
GCF of Numerators i.e. for 30,363,407 is 1
LCM of denominators i.e. for 36,21,412 is 25956.
Thus, GCF of Fractions is 1/25956.Finally, GCF of Fractions for 30/36, 363/21, 407/412 is 1/25956.