GCF of 3/90, 3/18, 6/42, 72/120
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3/90, 3/18, 6/42, 72/120 i.e 3/2520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3/90, 3/18, 6/42, 72/120.
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 3/90,3/18,6/42,72/120?
Given fractions are 3/90,3/18,6/42,72/120
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 3/90,3/18,6/42,72/120, numerators are 3,3,6,72
Denominators are 90,18,42,120
The GCF of 3,3,6,72 is 3 .
LCM of 90,18,42,120 is 2520.
The greatest common factor of 3/90,3/18,6/42,72/120 = [GCF of 3,3,6,72]/[LCM of 90,18,42,120]= 3/2520
Therefore, the GCF of 3/90,3/18,6/42,72/120 is 3/2520.
To find the highest common factor of 3,3,6,72, we have to find the factors of both numbers and list the highest common factor.
The factors of 3 are 1, 3
The factors of 3 are 1, 3
The factors of 6 are 1, 2, 3, 6
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The HCF of 3,3,6,72 is 3.
Lets's calculate GCF of 3,3,6,72
| 3 | 3, 3, 6, 72 |
| 1, 1, 2, 24 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 3,3,6,72 By Matching Biggest Common Factor Method
Now, list down the factors of 3
:1,3
Now, list down the factors of 3
:1,3
Now, list down the factors of 6
:1,2,3,6
Now, list down the factors of 72
:1,2,3,4,6,8,9,12,18,24,36,72
Greatest Common Factor
We found the factors 3,3,6,72 . The biggest common factor number is the GCF number.
So the greatest common factor 3,3,6,72 is 3.
Lets's calculate LCM of 90,18,42,120
| 2 | 90, 18, 42, 120 |
| 3 | 45, 9, 21, 60 |
| 3 | 15, 3, 7, 20 |
| 5 | 5, 1, 7, 20 |
| 1, 1, 7, 4 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 5 x 1 x 1 x 7 x 4 = 2520
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/2520
Therefore, the GCF of Fractions 3/90,3/18,6/42,72/120 is 3/2520
Least Common Multiple of 90,18,42,120 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 90,18,42,120 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(90,18,42,120) = 6
common factors(in case of two or more numbers have common factors) = 540
GCF(90,18,42,120) x common factors =6 x 540 = 3240
LCM(90,18,42,120) = ( 90 × 18 × 42 × 120 ) / 3240
LCM(90,18,42,120) = 8164800 / 3240
LCM(90,18,42,120) = 2520
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 3/90, 3/18, 6/42, 72/120
1. What is the HCF of 3,3,6,72?
The HCF of 3,3,6,72 is 3
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 3/90, 3/18, 6/42, 72/120?
Answer: GCF of Numerators as per given numbers 3/90, 3/18, 6/42, 72/120 is
GCF of Numerators i.e. for 3,3,6,72 is 3
LCM of denominators i.e. for 90,18,42,120 is 2520.
Thus, GCF of Fractions is 3/2520.Finally, GCF of Fractions for 3/90, 3/18, 6/42, 72/120 is 3/2520.