GCF of 56/84, 45/75, 60/98, 67/32
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 56/84, 45/75, 60/98, 67/32 i.e 1/117600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 56/84, 45/75, 60/98, 67/32.
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 56/84,45/75,60/98,67/32?
Given fractions are 56/84,45/75,60/98,67/32
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 56/84,45/75,60/98,67/32, numerators are 56,45,60,67
Denominators are 84,75,98,32
The GCF of 56,45,60,67 is 1 .
LCM of 84,75,98,32 is 117600.
The greatest common factor of 56/84,45/75,60/98,67/32 = [GCF of 56,45,60,67]/[LCM of 84,75,98,32]= 1/117600
Therefore, the GCF of 56/84,45/75,60/98,67/32 is 1/117600.
To find the highest common factor of 56,45,60,67, we have to find the factors of both numbers and list the highest common factor.
The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56
The factors of 45 are 1, 3, 5, 9, 15, 45
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The factors of 67 are 1, 67
The HCF of 56,45,60,67 is 1.
Lets's calculate GCF of 56,45,60,67
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 56,45,60,67 By Matching Biggest Common Factor Method
Now, list down the factors of 56
:1,2,4,7,8,14,28,56
Now, list down the factors of 45
:1,3,5,9,15,45
Now, list down the factors of 60
:1,2,3,4,5,6,10,12,15,20,30,60
Now, list down the factors of 67
:1,67
Greatest Common Factor
We found the factors 56,45,60,67 . The biggest common factor number is the GCF number.
So the greatest common factor 56,45,60,67 is 1.
Lets's calculate LCM of 84,75,98,32
| 2 | 84, 75, 98, 32 |
| 2 | 42, 75, 49, 16 |
| 3 | 21, 75, 49, 8 |
| 7 | 7, 25, 49, 8 |
| 1, 25, 7, 8 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 1 x 25 x 7 x 8 = 117600
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/117600
Therefore, the GCF of Fractions 56/84,45/75,60/98,67/32 is 1/117600
Least Common Multiple of 84,75,98,32 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 84,75,98,32 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,75,98,32) = 1
common factors(in case of two or more numbers have common factors) = 168
GCF(84,75,98,32) x common factors =1 x 168 = 168
LCM(84,75,98,32) = ( 84 × 75 × 98 × 32 ) / 168
LCM(84,75,98,32) = 19756800 / 168
LCM(84,75,98,32) = 117600
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 56/84, 45/75, 60/98, 67/32
1. What is the HCF of 56,45,60,67?
The HCF of 56,45,60,67 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 56/84, 45/75, 60/98, 67/32?
Answer: GCF of Numerators as per given numbers 56/84, 45/75, 60/98, 67/32 is
GCF of Numerators i.e. for 56,45,60,67 is 1
LCM of denominators i.e. for 84,75,98,32 is 117600.
Thus, GCF of Fractions is 1/117600.Finally, GCF of Fractions for 56/84, 45/75, 60/98, 67/32 is 1/117600.