GCF of 30/54, 74/42, 535/378
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 30/54, 74/42, 535/378 i.e 1/378 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/54, 74/42, 535/378.
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 30/54,74/42,535/378?
Given fractions are 30/54,74/42,535/378
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 30/54,74/42,535/378, numerators are 30,74,535
Denominators are 54,42,378
The GCF of 30,74,535 is 1 .
LCM of 54,42,378 is 378.
The greatest common factor of 30/54,74/42,535/378 = [GCF of 30,74,535]/[LCM of 54,42,378]= 1/378
Therefore, the GCF of 30/54,74/42,535/378 is 1/378.
To find the highest common factor of 30,74,535, we have to find the factors of both numbers and list the highest common factor.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 74 are 1, 2, 37, 74
The factors of 535 are 1, 5, 107, 535
The HCF of 30,74,535 is 1.
Lets's calculate GCF of 30,74,535
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 30,74,535 By Matching Biggest Common Factor Method
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 74
:1,2,37,74
Now, list down the factors of 535
:1,5,107,535
Greatest Common Factor
We found the factors 30,74,535 . The biggest common factor number is the GCF number.
So the greatest common factor 30,74,535 is 1.
Lets's calculate LCM of 54,42,378
| 2 | 54, 42, 378 |
| 3 | 27, 21, 189 |
| 3 | 9, 7, 63 |
| 3 | 3, 7, 21 |
| 7 | 1, 7, 7 |
| 1, 1, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 3 x 7 x 1 x 1 x 1 = 378
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/378
Therefore, the GCF of Fractions 30/54,74/42,535/378 is 1/378
Least Common Multiple of 54,42,378 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 54,42,378 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,42,378) = 6
common factors(in case of two or more numbers have common factors) = 378
GCF(54,42,378) x common factors =6 x 378 = 2268
LCM(54,42,378) = ( 54 × 42 × 378 ) / 2268
LCM(54,42,378) = 857304 / 2268
LCM(54,42,378) = 378
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FAQs on GCF of Fractions of 30/54, 74/42, 535/378
1. What is the HCF of 30,74,535?
The HCF of 30,74,535 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 30/54, 74/42, 535/378?
Answer: GCF of Numerators as per given numbers 30/54, 74/42, 535/378 is
GCF of Numerators i.e. for 30,74,535 is 1
LCM of denominators i.e. for 54,42,378 is 378.
Thus, GCF of Fractions is 1/378.Finally, GCF of Fractions for 30/54, 74/42, 535/378 is 1/378.