GCF of 742/470, 3006/159
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 742/470, 3006/159 i.e 2/74730 easily. The following is the detailed procedure to determine the greatest common factor of fractions 742/470, 3006/159.
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 742/470,3006/159?
Given fractions are 742/470,3006/159
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 742/470,3006/159, numerators are 742,3006
Denominators are 470,159
The GCF of 742,3006 is 2 .
LCM of 470,159 is 74730.
The greatest common factor of 742/470,3006/159 = [GCF of 742,3006]/[LCM of 470,159]= 2/74730
Therefore, the GCF of 742/470,3006/159 is 2/74730.
To find the highest common factor of 742,3006, we have to find the factors of both numbers and list the highest common factor.
The factors of 742 are 1, 2, 7, 14, 53, 106, 371, 742
The factors of 3006 are 1, 2, 3, 6, 9, 18, 167, 334, 501, 1002, 1503, 3006
The HCF of 742,3006 is 2.
Lets's calculate GCF of 742,3006
| 2 | 742, 3006 |
| 371, 1503 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 742,3006 By Matching Biggest Common Factor Method
Now, list down the factors of 742
:1,2,7,14,53,106,371,742
Now, list down the factors of 3006
:1,2,3,6,9,18,167,334,501,1002,1503,3006
Greatest Common Factor
We found the factors 742,3006 . The biggest common factor number is the GCF number.
So the greatest common factor 742,3006 is 2.
Lets's calculate LCM of 470,159
Given numbers has no common factors except 1. So, there LCM is their product i.e 74730
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/74730
Therefore, the GCF of Fractions 742/470,3006/159 is 2/74730
Least Common Multiple of 470,159 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 470,159 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(470,159) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(470,159) x common factors =1 x 1 = 1
LCM(470,159) = ( 470 × 159 ) / 1
LCM(470,159) = 74730 / 1
LCM(470,159) = 74730
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FAQs on GCF of Fractions of 742/470, 3006/159
1. What is the HCF of 742,3006?
The HCF of 742,3006 is 2
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 742/470, 3006/159?
Answer: GCF of Numerators as per given numbers 742/470, 3006/159 is
GCF of Numerators i.e. for 742,3006 is 2
LCM of denominators i.e. for 470,159 is 74730.
Thus, GCF of Fractions is 2/74730.Finally, GCF of Fractions for 742/470, 3006/159 is 2/74730.