GCF of 25/16, 22/75, 84/13, 17/104
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 25/16, 22/75, 84/13, 17/104 i.e 1/15600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 25/16, 22/75, 84/13, 17/104.
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 25/16,22/75,84/13,17/104?
Given fractions are 25/16,22/75,84/13,17/104
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 25/16,22/75,84/13,17/104, numerators are 25,22,84,17
Denominators are 16,75,13,104
The GCF of 25,22,84,17 is 1 .
LCM of 16,75,13,104 is 15600.
The greatest common factor of 25/16,22/75,84/13,17/104 = [GCF of 25,22,84,17]/[LCM of 16,75,13,104]= 1/15600
Therefore, the GCF of 25/16,22/75,84/13,17/104 is 1/15600.
To find the highest common factor of 25,22,84,17, we have to find the factors of both numbers and list the highest common factor.
The factors of 25 are 1, 5, 25
The factors of 22 are 1, 2, 11, 22
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 17 are 1, 17
The HCF of 25,22,84,17 is 1.
Lets's calculate GCF of 25,22,84,17
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 25,22,84,17 By Matching Biggest Common Factor Method
Now, list down the factors of 25
:1,5,25
Now, list down the factors of 22
:1,2,11,22
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
Now, list down the factors of 17
:1,17
Greatest Common Factor
We found the factors 25,22,84,17 . The biggest common factor number is the GCF number.
So the greatest common factor 25,22,84,17 is 1.
Lets's calculate LCM of 16,75,13,104
| 2 | 16, 75, 13, 104 |
| 2 | 8, 75, 13, 52 |
| 2 | 4, 75, 13, 26 |
| 13 | 2, 75, 13, 13 |
| 2, 75, 1, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 13 x 2 x 75 x 1 x 1 = 15600
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/15600
Therefore, the GCF of Fractions 25/16,22/75,84/13,17/104 is 1/15600
Least Common Multiple of 16,75,13,104 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 16,75,13,104 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(16,75,13,104) = 1
common factors(in case of two or more numbers have common factors) = 104
GCF(16,75,13,104) x common factors =1 x 104 = 104
LCM(16,75,13,104) = ( 16 × 75 × 13 × 104 ) / 104
LCM(16,75,13,104) = 1622400 / 104
LCM(16,75,13,104) = 15600
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 25/16, 22/75, 84/13, 17/104
1. What is the HCF of 25,22,84,17?
The HCF of 25,22,84,17 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 25/16, 22/75, 84/13, 17/104?
Answer: GCF of Numerators as per given numbers 25/16, 22/75, 84/13, 17/104 is
GCF of Numerators i.e. for 25,22,84,17 is 1
LCM of denominators i.e. for 16,75,13,104 is 15600.
Thus, GCF of Fractions is 1/15600.Finally, GCF of Fractions for 25/16, 22/75, 84/13, 17/104 is 1/15600.