GCF of 912/29, 342/489
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 912/29, 342/489 i.e 114/14181 easily. The following is the detailed procedure to determine the greatest common factor of fractions 912/29, 342/489.
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 912/29,342/489?
Given fractions are 912/29,342/489
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 912/29,342/489, numerators are 912,342
Denominators are 29,489
The GCF of 912,342 is 114 .
LCM of 29,489 is 14181.
The greatest common factor of 912/29,342/489 = [GCF of 912,342]/[LCM of 29,489]= 114/14181
Therefore, the GCF of 912/29,342/489 is 114/14181.
To find the highest common factor of 912,342, we have to find the factors of both numbers and list the highest common factor.
The factors of 912 are 1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 38, 48, 57, 76, 114, 152, 228, 304, 456, 912
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The HCF of 912,342 is 114.
Lets's calculate GCF of 912,342
| 2 | 912, 342 |
| 3 | 456, 171 |
| 19 | 152, 57 |
| 8, 3 |
∴ So the GCF of the given numbers is 2 x 3 x 19 = 114
Greatest Common Factor of 912,342 By Matching Biggest Common Factor Method
Now, list down the factors of 912
:1,2,3,4,6,8,12,16,19,24,38,48,57,76,114,152,228,304,456,912
Now, list down the factors of 342
:1,2,3,6,9,18,19,38,57,114,171,342
Greatest Common Factor
We found the factors 912,342 . The biggest common factor number is the GCF number.
So the greatest common factor 912,342 is 114.
Lets's calculate LCM of 29,489
Given numbers has no common factors except 1. So, there LCM is their product i.e 14181
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 114/14181
Therefore, the GCF of Fractions 912/29,342/489 is 114/14181
Least Common Multiple of 29,489 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 29,489 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(29,489) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(29,489) x common factors =1 x 1 = 1
LCM(29,489) = ( 29 × 489 ) / 1
LCM(29,489) = 14181 / 1
LCM(29,489) = 14181
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FAQs on GCF of Fractions of 912/29, 342/489
1. What is the HCF of 912,342?
The HCF of 912,342 is 114
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 912/29, 342/489?
Answer: GCF of Numerators as per given numbers 912/29, 342/489 is
GCF of Numerators i.e. for 912,342 is 114
LCM of denominators i.e. for 29,489 is 14181.
Thus, GCF of Fractions is 114/14181.Finally, GCF of Fractions for 912/29, 342/489 is 114/14181.