GCF of 28/42, 90/49, 345/53
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 28/42, 90/49, 345/53 i.e 1/15582 easily. The following is the detailed procedure to determine the greatest common factor of fractions 28/42, 90/49, 345/53.
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 28/42,90/49,345/53?
Given fractions are 28/42,90/49,345/53
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 28/42,90/49,345/53, numerators are 28,90,345
Denominators are 42,49,53
The GCF of 28,90,345 is 1 .
LCM of 42,49,53 is 15582.
The greatest common factor of 28/42,90/49,345/53 = [GCF of 28,90,345]/[LCM of 42,49,53]= 1/15582
Therefore, the GCF of 28/42,90/49,345/53 is 1/15582.
To find the highest common factor of 28,90,345, we have to find the factors of both numbers and list the highest common factor.
The factors of 28 are 1, 2, 4, 7, 14, 28
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The factors of 345 are 1, 3, 5, 15, 23, 69, 115, 345
The HCF of 28,90,345 is 1.
Lets's calculate GCF of 28,90,345
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 28,90,345 By Matching Biggest Common Factor Method
Now, list down the factors of 28
:1,2,4,7,14,28
Now, list down the factors of 90
:1,2,3,5,6,9,10,15,18,30,45,90
Now, list down the factors of 345
:1,3,5,15,23,69,115,345
Greatest Common Factor
We found the factors 28,90,345 . The biggest common factor number is the GCF number.
So the greatest common factor 28,90,345 is 1.
Lets's calculate LCM of 42,49,53
| 7 | 42, 49, 53 |
| 6, 7, 53 |
∴ So the LCM of the given numbers is 7 x 6 x 7 x 53 = 15582
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/15582
Therefore, the GCF of Fractions 28/42,90/49,345/53 is 1/15582
Least Common Multiple of 42,49,53 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 42,49,53 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,49,53) = 1
common factors(in case of two or more numbers have common factors) = 7
GCF(42,49,53) x common factors =1 x 7 = 7
LCM(42,49,53) = ( 42 × 49 × 53 ) / 7
LCM(42,49,53) = 109074 / 7
LCM(42,49,53) = 15582
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FAQs on GCF of Fractions of 28/42, 90/49, 345/53
1. What is the HCF of 28,90,345?
The HCF of 28,90,345 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 28/42, 90/49, 345/53?
Answer: GCF of Numerators as per given numbers 28/42, 90/49, 345/53 is
GCF of Numerators i.e. for 28,90,345 is 1
LCM of denominators i.e. for 42,49,53 is 15582.
Thus, GCF of Fractions is 1/15582.Finally, GCF of Fractions for 28/42, 90/49, 345/53 is 1/15582.