GCF of 19/64, 45/42, 30/48, 25/12
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 19/64, 45/42, 30/48, 25/12 i.e 1/1344 easily. The following is the detailed procedure to determine the greatest common factor of fractions 19/64, 45/42, 30/48, 25/12.
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 19/64,45/42,30/48,25/12?
Given fractions are 19/64,45/42,30/48,25/12
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 19/64,45/42,30/48,25/12, numerators are 19,45,30,25
Denominators are 64,42,48,12
The GCF of 19,45,30,25 is 1 .
LCM of 64,42,48,12 is 1344.
The greatest common factor of 19/64,45/42,30/48,25/12 = [GCF of 19,45,30,25]/[LCM of 64,42,48,12]= 1/1344
Therefore, the GCF of 19/64,45/42,30/48,25/12 is 1/1344.
To find the highest common factor of 19,45,30,25, we have to find the factors of both numbers and list the highest common factor.
The factors of 19 are 1, 19
The factors of 45 are 1, 3, 5, 9, 15, 45
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 25 are 1, 5, 25
The HCF of 19,45,30,25 is 1.
Lets's calculate GCF of 19,45,30,25
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 19,45,30,25 By Matching Biggest Common Factor Method
Now, list down the factors of 19
:1,19
Now, list down the factors of 45
:1,3,5,9,15,45
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 25
:1,5,25
Greatest Common Factor
We found the factors 19,45,30,25 . The biggest common factor number is the GCF number.
So the greatest common factor 19,45,30,25 is 1.
Lets's calculate LCM of 64,42,48,12
| 2 | 64, 42, 48, 12 |
| 2 | 32, 21, 24, 6 |
| 2 | 16, 21, 12, 3 |
| 2 | 8, 21, 6, 3 |
| 3 | 4, 21, 3, 3 |
| 4, 7, 1, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 3 x 4 x 7 x 1 x 1 = 1344
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1344
Therefore, the GCF of Fractions 19/64,45/42,30/48,25/12 is 1/1344
Least Common Multiple of 64,42,48,12 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 64,42,48,12 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(64,42,48,12) = 2
common factors(in case of two or more numbers have common factors) = 576
GCF(64,42,48,12) x common factors =2 x 576 = 1152
LCM(64,42,48,12) = ( 64 × 42 × 48 × 12 ) / 1152
LCM(64,42,48,12) = 1548288 / 1152
LCM(64,42,48,12) = 1344
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 19/64, 45/42, 30/48, 25/12
1. What is the HCF of 19,45,30,25?
The HCF of 19,45,30,25 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 19/64, 45/42, 30/48, 25/12?
Answer: GCF of Numerators as per given numbers 19/64, 45/42, 30/48, 25/12 is
GCF of Numerators i.e. for 19,45,30,25 is 1
LCM of denominators i.e. for 64,42,48,12 is 1344.
Thus, GCF of Fractions is 1/1344.Finally, GCF of Fractions for 19/64, 45/42, 30/48, 25/12 is 1/1344.