GCF of 34/78, 192/92, 289/299
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 34/78, 192/92, 289/299 i.e 1/3588 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/78, 192/92, 289/299.
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 34/78,192/92,289/299?
Given fractions are 34/78,192/92,289/299
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 34/78,192/92,289/299, numerators are 34,192,289
Denominators are 78,92,299
The GCF of 34,192,289 is 1 .
LCM of 78,92,299 is 3588.
The greatest common factor of 34/78,192/92,289/299 = [GCF of 34,192,289]/[LCM of 78,92,299]= 1/3588
Therefore, the GCF of 34/78,192/92,289/299 is 1/3588.
To find the highest common factor of 34,192,289, we have to find the factors of both numbers and list the highest common factor.
The factors of 34 are 1, 2, 17, 34
The factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
The factors of 289 are 1, 17, 289
The HCF of 34,192,289 is 1.
Lets's calculate GCF of 34,192,289
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 34,192,289 By Matching Biggest Common Factor Method
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 192
:1,2,3,4,6,8,12,16,24,32,48,64,96,192
Now, list down the factors of 289
:1,17,289
Greatest Common Factor
We found the factors 34,192,289 . The biggest common factor number is the GCF number.
So the greatest common factor 34,192,289 is 1.
Lets's calculate LCM of 78,92,299
| 2 | 78, 92, 299 |
| 13 | 39, 46, 299 |
| 23 | 3, 46, 23 |
| 3, 2, 1 |
∴ So the LCM of the given numbers is 2 x 13 x 23 x 3 x 2 x 1 = 3588
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3588
Therefore, the GCF of Fractions 34/78,192/92,289/299 is 1/3588
Least Common Multiple of 78,92,299 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 78,92,299 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,92,299) = 1
common factors(in case of two or more numbers have common factors) = 598
GCF(78,92,299) x common factors =1 x 598 = 598
LCM(78,92,299) = ( 78 × 92 × 299 ) / 598
LCM(78,92,299) = 2145624 / 598
LCM(78,92,299) = 3588
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FAQs on GCF of Fractions of 34/78, 192/92, 289/299
1. What is the HCF of 34,192,289?
The HCF of 34,192,289 is 1
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 34/78, 192/92, 289/299?
Answer: GCF of Numerators as per given numbers 34/78, 192/92, 289/299 is
GCF of Numerators i.e. for 34,192,289 is 1
LCM of denominators i.e. for 78,92,299 is 3588.
Thus, GCF of Fractions is 1/3588.Finally, GCF of Fractions for 34/78, 192/92, 289/299 is 1/3588.