GCF of 492/20, 972/3971
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 492/20, 972/3971 i.e 12/79420 easily. The following is the detailed procedure to determine the greatest common factor of fractions 492/20, 972/3971.
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 492/20,972/3971?
Given fractions are 492/20,972/3971
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 492/20,972/3971, numerators are 492,972
Denominators are 20,3971
The GCF of 492,972 is 12 .
LCM of 20,3971 is 79420.
The greatest common factor of 492/20,972/3971 = [GCF of 492,972]/[LCM of 20,3971]= 12/79420
Therefore, the GCF of 492/20,972/3971 is 12/79420.
To find the highest common factor of 492,972, we have to find the factors of both numbers and list the highest common factor.
The factors of 492 are 1, 2, 3, 4, 6, 12, 41, 82, 123, 164, 246, 492
The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
The HCF of 492,972 is 12.
Lets's calculate GCF of 492,972
| 2 | 492, 972 |
| 2 | 246, 486 |
| 3 | 123, 243 |
| 41, 81 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 492,972 By Matching Biggest Common Factor Method
Now, list down the factors of 492
:1,2,3,4,6,12,41,82,123,164,246,492
Now, list down the factors of 972
:1,2,3,4,6,9,12,18,27,36,54,81,108,162,243,324,486,972
Greatest Common Factor
We found the factors 492,972 . The biggest common factor number is the GCF number.
So the greatest common factor 492,972 is 12.
Lets's calculate LCM of 20,3971
Given numbers has no common factors except 1. So, there LCM is their product i.e 79420
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/79420
Therefore, the GCF of Fractions 492/20,972/3971 is 12/79420
Least Common Multiple of 20,3971 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 20,3971 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(20,3971) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(20,3971) x common factors =1 x 1 = 1
LCM(20,3971) = ( 20 × 3971 ) / 1
LCM(20,3971) = 79420 / 1
LCM(20,3971) = 79420
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FAQs on GCF of Fractions of 492/20, 972/3971
1. What is the HCF of 492,972?
The HCF of 492,972 is 12
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 492/20, 972/3971?
Answer: GCF of Numerators as per given numbers 492/20, 972/3971 is
GCF of Numerators i.e. for 492,972 is 12
LCM of denominators i.e. for 20,3971 is 79420.
Thus, GCF of Fractions is 12/79420.Finally, GCF of Fractions for 492/20, 972/3971 is 12/79420.