GCF of 133/34, 609/224
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 133/34, 609/224 i.e 7/3808 easily. The following is the detailed procedure to determine the greatest common factor of fractions 133/34, 609/224.
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 133/34,609/224?
Given fractions are 133/34,609/224
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 133/34,609/224, numerators are 133,609
Denominators are 34,224
The GCF of 133,609 is 7 .
LCM of 34,224 is 3808.
The greatest common factor of 133/34,609/224 = [GCF of 133,609]/[LCM of 34,224]= 7/3808
Therefore, the GCF of 133/34,609/224 is 7/3808.
To find the highest common factor of 133,609, we have to find the factors of both numbers and list the highest common factor.
The factors of 133 are 1, 7, 19, 133
The factors of 609 are 1, 3, 7, 21, 29, 87, 203, 609
The HCF of 133,609 is 7.
Lets's calculate GCF of 133,609
| 7 | 133, 609 |
| 19, 87 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 133,609 By Matching Biggest Common Factor Method
Now, list down the factors of 133
:1,7,19,133
Now, list down the factors of 609
:1,3,7,21,29,87,203,609
Greatest Common Factor
We found the factors 133,609 . The biggest common factor number is the GCF number.
So the greatest common factor 133,609 is 7.
Lets's calculate LCM of 34,224
| 2 | 34, 224 |
| 17, 112 |
∴ So the LCM of the given numbers is 2 x 17 x 112 = 3808
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/3808
Therefore, the GCF of Fractions 133/34,609/224 is 7/3808
Least Common Multiple of 34,224 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 34,224 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,224) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(34,224) x common factors =2 x 1 = 2
LCM(34,224) = ( 34 × 224 ) / 2
LCM(34,224) = 7616 / 2
LCM(34,224) = 3808
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FAQs on GCF of Fractions of 133/34, 609/224
1. What is the HCF of 133,609?
The HCF of 133,609 is 7
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 133/34, 609/224?
Answer: GCF of Numerators as per given numbers 133/34, 609/224 is
GCF of Numerators i.e. for 133,609 is 7
LCM of denominators i.e. for 34,224 is 3808.
Thus, GCF of Fractions is 7/3808.Finally, GCF of Fractions for 133/34, 609/224 is 7/3808.