GCF of 19/85, 76/17, 89/36, 65/40
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 19/85, 76/17, 89/36, 65/40 i.e 1/6120 easily. The following is the detailed procedure to determine the greatest common factor of fractions 19/85, 76/17, 89/36, 65/40.
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 19/85,76/17,89/36,65/40?
Given fractions are 19/85,76/17,89/36,65/40
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 19/85,76/17,89/36,65/40, numerators are 19,76,89,65
Denominators are 85,17,36,40
The GCF of 19,76,89,65 is 1 .
LCM of 85,17,36,40 is 6120.
The greatest common factor of 19/85,76/17,89/36,65/40 = [GCF of 19,76,89,65]/[LCM of 85,17,36,40]= 1/6120
Therefore, the GCF of 19/85,76/17,89/36,65/40 is 1/6120.
To find the highest common factor of 19,76,89,65, we have to find the factors of both numbers and list the highest common factor.
The factors of 19 are 1, 19
The factors of 76 are 1, 2, 4, 19, 38, 76
The factors of 89 are 1, 89
The factors of 65 are 1, 5, 13, 65
The HCF of 19,76,89,65 is 1.
Lets's calculate GCF of 19,76,89,65
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 19,76,89,65 By Matching Biggest Common Factor Method
Now, list down the factors of 19
:1,19
Now, list down the factors of 76
:1,2,4,19,38,76
Now, list down the factors of 89
:1,89
Now, list down the factors of 65
:1,5,13,65
Greatest Common Factor
We found the factors 19,76,89,65 . The biggest common factor number is the GCF number.
So the greatest common factor 19,76,89,65 is 1.
Lets's calculate LCM of 85,17,36,40
| 2 | 85, 17, 36, 40 |
| 2 | 85, 17, 18, 20 |
| 5 | 85, 17, 9, 10 |
| 17 | 17, 17, 9, 2 |
| 1, 1, 9, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 17 x 1 x 1 x 9 x 2 = 6120
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6120
Therefore, the GCF of Fractions 19/85,76/17,89/36,65/40 is 1/6120
Least Common Multiple of 85,17,36,40 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 85,17,36,40 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(85,17,36,40) = 1
common factors(in case of two or more numbers have common factors) = 340
GCF(85,17,36,40) x common factors =1 x 340 = 340
LCM(85,17,36,40) = ( 85 × 17 × 36 × 40 ) / 340
LCM(85,17,36,40) = 2080800 / 340
LCM(85,17,36,40) = 6120
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 19/85, 76/17, 89/36, 65/40
1. What is the HCF of 19,76,89,65?
The HCF of 19,76,89,65 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 19/85, 76/17, 89/36, 65/40?
Answer: GCF of Numerators as per given numbers 19/85, 76/17, 89/36, 65/40 is
GCF of Numerators i.e. for 19,76,89,65 is 1
LCM of denominators i.e. for 85,17,36,40 is 6120.
Thus, GCF of Fractions is 1/6120.Finally, GCF of Fractions for 19/85, 76/17, 89/36, 65/40 is 1/6120.