GCF of 392/32, 972/314
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 392/32, 972/314 i.e 4/5024 easily. The following is the detailed procedure to determine the greatest common factor of fractions 392/32, 972/314.
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 392/32,972/314?
Given fractions are 392/32,972/314
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 392/32,972/314, numerators are 392,972
Denominators are 32,314
The GCF of 392,972 is 4 .
LCM of 32,314 is 5024.
The greatest common factor of 392/32,972/314 = [GCF of 392,972]/[LCM of 32,314]= 4/5024
Therefore, the GCF of 392/32,972/314 is 4/5024.
To find the highest common factor of 392,972, we have to find the factors of both numbers and list the highest common factor.
The factors of 392 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392
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 392,972 is 4.
Lets's calculate GCF of 392,972
| 2 | 392, 972 |
| 2 | 196, 486 |
| 98, 243 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 392,972 By Matching Biggest Common Factor Method
Now, list down the factors of 392
:1,2,4,7,8,14,28,49,56,98,196,392
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 392,972 . The biggest common factor number is the GCF number.
So the greatest common factor 392,972 is 4.
Lets's calculate LCM of 32,314
| 2 | 32, 314 |
| 16, 157 |
∴ So the LCM of the given numbers is 2 x 16 x 157 = 5024
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/5024
Therefore, the GCF of Fractions 392/32,972/314 is 4/5024
Least Common Multiple of 32,314 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 32,314 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,314) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(32,314) x common factors =2 x 1 = 2
LCM(32,314) = ( 32 × 314 ) / 2
LCM(32,314) = 10048 / 2
LCM(32,314) = 5024
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FAQs on GCF of Fractions of 392/32, 972/314
1. What is the HCF of 392,972?
The HCF of 392,972 is 4
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 392/32, 972/314?
Answer: GCF of Numerators as per given numbers 392/32, 972/314 is
GCF of Numerators i.e. for 392,972 is 4
LCM of denominators i.e. for 32,314 is 5024.
Thus, GCF of Fractions is 4/5024.Finally, GCF of Fractions for 392/32, 972/314 is 4/5024.