Use our free GCF of Fractions Calculator tool to compute the GCF of 8/65, 42/74, 43/549, 580/492 i.e 1/216536580 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8/65, 42/74, 43/549, 580/492.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 8/65,42/74,43/549,580/492
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 8/65,42/74,43/549,580/492, numerators are 8,42,43,580
Denominators are 65,74,549,492
The GCF of 8,42,43,580 is 1 .
LCM of 65,74,549,492 is 216536580.
The greatest common factor of 8/65,42/74,43/549,580/492 = [GCF of 8,42,43,580]/[LCM of 65,74,549,492]= 1/216536580
Therefore, the GCF of 8/65,42/74,43/549,580/492 is 1/216536580.
To find the highest common factor of 8,42,43,580, we have to find the factors of both numbers and list the highest common factor.
The factors of 8 are 1, 2, 4, 8
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 43 are 1, 43
The factors of 580 are 1, 2, 4, 5, 10, 20, 29, 58, 116, 145, 290, 580
The HCF of 8,42,43,580 is 1.
Lets's calculate GCF of 8,42,43,580
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 8
:1,2,4,8
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 43
:1,43
Now, list down the factors of 580
:1,2,4,5,10,20,29,58,116,145,290,580
Greatest Common Factor
We found the factors 8,42,43,580 . The biggest common factor number is the GCF number.
So the greatest common factor 8,42,43,580 is 1.
Lets's calculate LCM of 65,74,549,492
2 | 65, 74, 549, 492 |
3 | 65, 37, 549, 246 |
65, 37, 183, 82 |
∴ So the LCM of the given numbers is 2 x 3 x 65 x 37 x 183 x 82 = 216536580
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/216536580
Therefore, the GCF of Fractions 8/65,42/74,43/549,580/492 is 1/216536580
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 65,74,549,492 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,74,549,492) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(65,74,549,492) x common factors =1 x 6 = 6
LCM(65,74,549,492) = ( 65 × 74 × 549 × 492 ) / 6
LCM(65,74,549,492) = 1299219480 / 6
LCM(65,74,549,492) = 216536580
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 8,42,43,580?
The HCF of 8,42,43,580 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 8/65, 42/74, 43/549, 580/492?
Answer: GCF of Numerators as per given numbers 8/65, 42/74, 43/549, 580/492 is
GCF of Numerators i.e. for 8,42,43,580 is 1
LCM of denominators i.e. for 65,74,549,492 is 216536580.
Thus, GCF of Fractions is 1/216536580.Finally, GCF of Fractions for 8/65, 42/74, 43/549, 580/492 is 1/216536580.