GCF of 34/72, 52/136, 582/306
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 34/72, 52/136, 582/306 i.e 2/1224 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/72, 52/136, 582/306.
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 34/72,52/136,582/306?
Given fractions are 34/72,52/136,582/306
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 34/72,52/136,582/306, numerators are 34,52,582
Denominators are 72,136,306
The GCF of 34,52,582 is 2 .
LCM of 72,136,306 is 1224.
The greatest common factor of 34/72,52/136,582/306 = [GCF of 34,52,582]/[LCM of 72,136,306]= 2/1224
Therefore, the GCF of 34/72,52/136,582/306 is 2/1224.
To find the highest common factor of 34,52,582, 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 52 are 1, 2, 4, 13, 26, 52
The factors of 582 are 1, 2, 3, 6, 97, 194, 291, 582
The HCF of 34,52,582 is 2.
Lets's calculate GCF of 34,52,582
| 2 | 34, 52, 582 |
| 17, 26, 291 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 34,52,582 By Matching Biggest Common Factor Method
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 52
:1,2,4,13,26,52
Now, list down the factors of 582
:1,2,3,6,97,194,291,582
Greatest Common Factor
We found the factors 34,52,582 . The biggest common factor number is the GCF number.
So the greatest common factor 34,52,582 is 2.
Lets's calculate LCM of 72,136,306
| 2 | 72, 136, 306 |
| 2 | 36, 68, 153 |
| 2 | 18, 34, 153 |
| 3 | 9, 17, 153 |
| 3 | 3, 17, 51 |
| 17 | 1, 17, 17 |
| 1, 1, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 3 x 17 x 1 x 1 x 1 = 1224
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1224
Therefore, the GCF of Fractions 34/72,52/136,582/306 is 2/1224
Least Common Multiple of 72,136,306 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 72,136,306 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(72,136,306) = 2
common factors(in case of two or more numbers have common factors) = 1224
GCF(72,136,306) x common factors =2 x 1224 = 2448
LCM(72,136,306) = ( 72 × 136 × 306 ) / 2448
LCM(72,136,306) = 2996352 / 2448
LCM(72,136,306) = 1224
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FAQs on GCF of Fractions of 34/72, 52/136, 582/306
1. What is the HCF of 34,52,582?
The HCF of 34,52,582 is 2
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 34/72, 52/136, 582/306?
Answer: GCF of Numerators as per given numbers 34/72, 52/136, 582/306 is
GCF of Numerators i.e. for 34,52,582 is 2
LCM of denominators i.e. for 72,136,306 is 1224.
Thus, GCF of Fractions is 2/1224.Finally, GCF of Fractions for 34/72, 52/136, 582/306 is 2/1224.