GCF of 2/74, 40/39, 35/390, 438/165
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2/74, 40/39, 35/390, 438/165 i.e 1/158730 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2/74, 40/39, 35/390, 438/165.
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 2/74,40/39,35/390,438/165?
Given fractions are 2/74,40/39,35/390,438/165
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 2/74,40/39,35/390,438/165, numerators are 2,40,35,438
Denominators are 74,39,390,165
The GCF of 2,40,35,438 is 1 .
LCM of 74,39,390,165 is 158730.
The greatest common factor of 2/74,40/39,35/390,438/165 = [GCF of 2,40,35,438]/[LCM of 74,39,390,165]= 1/158730
Therefore, the GCF of 2/74,40/39,35/390,438/165 is 1/158730.
To find the highest common factor of 2,40,35,438, we have to find the factors of both numbers and list the highest common factor.
The factors of 2 are 1, 2
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 35 are 1, 5, 7, 35
The factors of 438 are 1, 2, 3, 6, 73, 146, 219, 438
The HCF of 2,40,35,438 is 1.
Lets's calculate GCF of 2,40,35,438
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 2,40,35,438 By Matching Biggest Common Factor Method
Now, list down the factors of 2
:1,2
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 35
:1,5,7,35
Now, list down the factors of 438
:1,2,3,6,73,146,219,438
Greatest Common Factor
We found the factors 2,40,35,438 . The biggest common factor number is the GCF number.
So the greatest common factor 2,40,35,438 is 1.
Lets's calculate LCM of 74,39,390,165
| 2 | 74, 39, 390, 165 |
| 3 | 37, 39, 195, 165 |
| 5 | 37, 13, 65, 55 |
| 13 | 37, 13, 13, 11 |
| 37, 1, 1, 11 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 13 x 37 x 1 x 1 x 11 = 158730
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/158730
Therefore, the GCF of Fractions 2/74,40/39,35/390,438/165 is 1/158730
Least Common Multiple of 74,39,390,165 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 74,39,390,165 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,39,390,165) = 1
common factors(in case of two or more numbers have common factors) = 1170
GCF(74,39,390,165) x common factors =1 x 1170 = 1170
LCM(74,39,390,165) = ( 74 × 39 × 390 × 165 ) / 1170
LCM(74,39,390,165) = 185714100 / 1170
LCM(74,39,390,165) = 158730
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 2/74, 40/39, 35/390, 438/165
1. What is the HCF of 2,40,35,438?
The HCF of 2,40,35,438 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 2/74, 40/39, 35/390, 438/165?
Answer: GCF of Numerators as per given numbers 2/74, 40/39, 35/390, 438/165 is
GCF of Numerators i.e. for 2,40,35,438 is 1
LCM of denominators i.e. for 74,39,390,165 is 158730.
Thus, GCF of Fractions is 1/158730.Finally, GCF of Fractions for 2/74, 40/39, 35/390, 438/165 is 1/158730.