GCF of 513/134, 222/154
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 513/134, 222/154 i.e 3/10318 easily. The following is the detailed procedure to determine the greatest common factor of fractions 513/134, 222/154.
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 513/134,222/154?
Given fractions are 513/134,222/154
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 513/134,222/154, numerators are 513,222
Denominators are 134,154
The GCF of 513,222 is 3 .
LCM of 134,154 is 10318.
The greatest common factor of 513/134,222/154 = [GCF of 513,222]/[LCM of 134,154]= 3/10318
Therefore, the GCF of 513/134,222/154 is 3/10318.
To find the highest common factor of 513,222, we have to find the factors of both numbers and list the highest common factor.
The factors of 513 are 1, 3, 9, 19, 27, 57, 171, 513
The factors of 222 are 1, 2, 3, 6, 37, 74, 111, 222
The HCF of 513,222 is 3.
Lets's calculate GCF of 513,222
| 3 | 513, 222 |
| 171, 74 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 513,222 By Matching Biggest Common Factor Method
Now, list down the factors of 513
:1,3,9,19,27,57,171,513
Now, list down the factors of 222
:1,2,3,6,37,74,111,222
Greatest Common Factor
We found the factors 513,222 . The biggest common factor number is the GCF number.
So the greatest common factor 513,222 is 3.
Lets's calculate LCM of 134,154
| 2 | 134, 154 |
| 67, 77 |
∴ So the LCM of the given numbers is 2 x 67 x 77 = 10318
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/10318
Therefore, the GCF of Fractions 513/134,222/154 is 3/10318
Least Common Multiple of 134,154 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 134,154 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(134,154) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(134,154) x common factors =2 x 1 = 2
LCM(134,154) = ( 134 × 154 ) / 2
LCM(134,154) = 20636 / 2
LCM(134,154) = 10318
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FAQs on GCF of Fractions of 513/134, 222/154
1. What is the HCF of 513,222?
The HCF of 513,222 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 513/134, 222/154?
Answer: GCF of Numerators as per given numbers 513/134, 222/154 is
GCF of Numerators i.e. for 513,222 is 3
LCM of denominators i.e. for 134,154 is 10318.
Thus, GCF of Fractions is 3/10318.Finally, GCF of Fractions for 513/134, 222/154 is 3/10318.