GCF of 59/34, 64/39, 91/72, 65/624
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 59/34, 64/39, 91/72, 65/624 i.e 1/31824 easily. The following is the detailed procedure to determine the greatest common factor of fractions 59/34, 64/39, 91/72, 65/624.
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 59/34,64/39,91/72,65/624?
Given fractions are 59/34,64/39,91/72,65/624
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 59/34,64/39,91/72,65/624, numerators are 59,64,91,65
Denominators are 34,39,72,624
The GCF of 59,64,91,65 is 1 .
LCM of 34,39,72,624 is 31824.
The greatest common factor of 59/34,64/39,91/72,65/624 = [GCF of 59,64,91,65]/[LCM of 34,39,72,624]= 1/31824
Therefore, the GCF of 59/34,64/39,91/72,65/624 is 1/31824.
To find the highest common factor of 59,64,91,65, we have to find the factors of both numbers and list the highest common factor.
The factors of 59 are 1, 59
The factors of 64 are 1, 2, 4, 8, 16, 32, 64
The factors of 91 are 1, 7, 13, 91
The factors of 65 are 1, 5, 13, 65
The HCF of 59,64,91,65 is 1.
Lets's calculate GCF of 59,64,91,65
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 59,64,91,65 By Matching Biggest Common Factor Method
Now, list down the factors of 59
:1,59
Now, list down the factors of 64
:1,2,4,8,16,32,64
Now, list down the factors of 91
:1,7,13,91
Now, list down the factors of 65
:1,5,13,65
Greatest Common Factor
We found the factors 59,64,91,65 . The biggest common factor number is the GCF number.
So the greatest common factor 59,64,91,65 is 1.
Lets's calculate LCM of 34,39,72,624
| 2 | 34, 39, 72, 624 |
| 2 | 17, 39, 36, 312 |
| 2 | 17, 39, 18, 156 |
| 3 | 17, 39, 9, 78 |
| 13 | 17, 13, 3, 26 |
| 17, 1, 3, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 13 x 17 x 1 x 3 x 2 = 31824
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/31824
Therefore, the GCF of Fractions 59/34,64/39,91/72,65/624 is 1/31824
Least Common Multiple of 34,39,72,624 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 34,39,72,624 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,39,72,624) = 1
common factors(in case of two or more numbers have common factors) = 1872
GCF(34,39,72,624) x common factors =1 x 1872 = 1872
LCM(34,39,72,624) = ( 34 × 39 × 72 × 624 ) / 1872
LCM(34,39,72,624) = 59574528 / 1872
LCM(34,39,72,624) = 31824
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FAQs on GCF of Fractions of 59/34, 64/39, 91/72, 65/624
1. What is the HCF of 59,64,91,65?
The HCF of 59,64,91,65 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 59/34, 64/39, 91/72, 65/624?
Answer: GCF of Numerators as per given numbers 59/34, 64/39, 91/72, 65/624 is
GCF of Numerators i.e. for 59,64,91,65 is 1
LCM of denominators i.e. for 34,39,72,624 is 31824.
Thus, GCF of Fractions is 1/31824.Finally, GCF of Fractions for 59/34, 64/39, 91/72, 65/624 is 1/31824.