GCF of 153/342, 189/416
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 153/342, 189/416 i.e 9/71136 easily. The following is the detailed procedure to determine the greatest common factor of fractions 153/342, 189/416.
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 153/342,189/416?
Given fractions are 153/342,189/416
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 153/342,189/416, numerators are 153,189
Denominators are 342,416
The GCF of 153,189 is 9 .
LCM of 342,416 is 71136.
The greatest common factor of 153/342,189/416 = [GCF of 153,189]/[LCM of 342,416]= 9/71136
Therefore, the GCF of 153/342,189/416 is 9/71136.
To find the highest common factor of 153,189, we have to find the factors of both numbers and list the highest common factor.
The factors of 153 are 1, 3, 9, 17, 51, 153
The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189
The HCF of 153,189 is 9.
Lets's calculate GCF of 153,189
| 3 | 153, 189 |
| 3 | 51, 63 |
| 17, 21 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 153,189 By Matching Biggest Common Factor Method
Now, list down the factors of 153
:1,3,9,17,51,153
Now, list down the factors of 189
:1,3,7,9,21,27,63,189
Greatest Common Factor
We found the factors 153,189 . The biggest common factor number is the GCF number.
So the greatest common factor 153,189 is 9.
Lets's calculate LCM of 342,416
| 2 | 342, 416 |
| 171, 208 |
∴ So the LCM of the given numbers is 2 x 171 x 208 = 71136
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/71136
Therefore, the GCF of Fractions 153/342,189/416 is 9/71136
Least Common Multiple of 342,416 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 342,416 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(342,416) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(342,416) x common factors =2 x 1 = 2
LCM(342,416) = ( 342 × 416 ) / 2
LCM(342,416) = 142272 / 2
LCM(342,416) = 71136
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FAQs on GCF of Fractions of 153/342, 189/416
1. What is the HCF of 153,189?
The HCF of 153,189 is 9
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 153/342, 189/416?
Answer: GCF of Numerators as per given numbers 153/342, 189/416 is
GCF of Numerators i.e. for 153,189 is 9
LCM of denominators i.e. for 342,416 is 71136.
Thus, GCF of Fractions is 9/71136.Finally, GCF of Fractions for 153/342, 189/416 is 9/71136.