GCF of 92/25, 72/17, 72/22, 18/31
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 92/25, 72/17, 72/22, 18/31 i.e 2/289850 easily. The following is the detailed procedure to determine the greatest common factor of fractions 92/25, 72/17, 72/22, 18/31.
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 92/25,72/17,72/22,18/31?
Given fractions are 92/25,72/17,72/22,18/31
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 92/25,72/17,72/22,18/31, numerators are 92,72,72,18
Denominators are 25,17,22,31
The GCF of 92,72,72,18 is 2 .
LCM of 25,17,22,31 is 289850.
The greatest common factor of 92/25,72/17,72/22,18/31 = [GCF of 92,72,72,18]/[LCM of 25,17,22,31]= 2/289850
Therefore, the GCF of 92/25,72/17,72/22,18/31 is 2/289850.
To find the highest common factor of 92,72,72,18, we have to find the factors of both numbers and list the highest common factor.
The factors of 92 are 1, 2, 4, 23, 46, 92
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The factors of 18 are 1, 2, 3, 6, 9, 18
The HCF of 92,72,72,18 is 2.
Lets's calculate GCF of 92,72,72,18
| 2 | 92, 72, 72, 18 |
| 46, 36, 36, 9 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 92,72,72,18 By Matching Biggest Common Factor Method
Now, list down the factors of 92
:1,2,4,23,46,92
Now, list down the factors of 72
:1,2,3,4,6,8,9,12,18,24,36,72
Now, list down the factors of 72
:1,2,3,4,6,8,9,12,18,24,36,72
Now, list down the factors of 18
:1,2,3,6,9,18
Greatest Common Factor
We found the factors 92,72,72,18 . The biggest common factor number is the GCF number.
So the greatest common factor 92,72,72,18 is 2.
Lets's calculate LCM of 25,17,22,31
Given numbers has no common factors except 1. So, there LCM is their product i.e 289850
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/289850
Therefore, the GCF of Fractions 92/25,72/17,72/22,18/31 is 2/289850
Least Common Multiple of 25,17,22,31 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 25,17,22,31 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(25,17,22,31) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(25,17,22,31) x common factors =1 x 1 = 1
LCM(25,17,22,31) = ( 25 × 17 × 22 × 31 ) / 1
LCM(25,17,22,31) = 289850 / 1
LCM(25,17,22,31) = 289850
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 92/25, 72/17, 72/22, 18/31
1. What is the HCF of 92,72,72,18?
The HCF of 92,72,72,18 is 2
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 92/25, 72/17, 72/22, 18/31?
Answer: GCF of Numerators as per given numbers 92/25, 72/17, 72/22, 18/31 is
GCF of Numerators i.e. for 92,72,72,18 is 2
LCM of denominators i.e. for 25,17,22,31 is 289850.
Thus, GCF of Fractions is 2/289850.Finally, GCF of Fractions for 92/25, 72/17, 72/22, 18/31 is 2/289850.