GCF of 45/21, 52/42, 23/14
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 45/21, 52/42, 23/14 i.e 1/42 easily. The following is the detailed procedure to determine the greatest common factor of fractions 45/21, 52/42, 23/14.
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 45/21,52/42,23/14?
Given fractions are 45/21,52/42,23/14
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 45/21,52/42,23/14, numerators are 45,52,23
Denominators are 21,42,14
The GCF of 45,52,23 is 1 .
LCM of 21,42,14 is 42.
The greatest common factor of 45/21,52/42,23/14 = [GCF of 45,52,23]/[LCM of 21,42,14]= 1/42
Therefore, the GCF of 45/21,52/42,23/14 is 1/42.
To find the highest common factor of 45,52,23, we have to find the factors of both numbers and list the highest common factor.
The factors of 45 are 1, 3, 5, 9, 15, 45
The factors of 52 are 1, 2, 4, 13, 26, 52
The factors of 23 are 1, 23
The HCF of 45,52,23 is 1.
Lets's calculate GCF of 45,52,23
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 45,52,23 By Matching Biggest Common Factor Method
Now, list down the factors of 45
:1,3,5,9,15,45
Now, list down the factors of 52
:1,2,4,13,26,52
Now, list down the factors of 23
:1,23
Greatest Common Factor
We found the factors 45,52,23 . The biggest common factor number is the GCF number.
So the greatest common factor 45,52,23 is 1.
Lets's calculate LCM of 21,42,14
| 2 | 21, 42, 14 |
| 3 | 21, 21, 7 |
| 7 | 7, 7, 7 |
| 1, 1, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 1 x 1 x 1 = 42
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/42
Therefore, the GCF of Fractions 45/21,52/42,23/14 is 1/42
Least Common Multiple of 21,42,14 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 21,42,14 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,42,14) = 7
common factors(in case of two or more numbers have common factors) = 42
GCF(21,42,14) x common factors =7 x 42 = 294
LCM(21,42,14) = ( 21 × 42 × 14 ) / 294
LCM(21,42,14) = 12348 / 294
LCM(21,42,14) = 42
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FAQs on GCF of Fractions of 45/21, 52/42, 23/14
1. What is the HCF of 45,52,23?
The HCF of 45,52,23 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 45/21, 52/42, 23/14?
Answer: GCF of Numerators as per given numbers 45/21, 52/42, 23/14 is
GCF of Numerators i.e. for 45,52,23 is 1
LCM of denominators i.e. for 21,42,14 is 42.
Thus, GCF of Fractions is 1/42.Finally, GCF of Fractions for 45/21, 52/42, 23/14 is 1/42.