GCF of 35/96, 16/64, 684/28
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 35/96, 16/64, 684/28 i.e 1/1344 easily. The following is the detailed procedure to determine the greatest common factor of fractions 35/96, 16/64, 684/28.
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 35/96,16/64,684/28?
Given fractions are 35/96,16/64,684/28
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 35/96,16/64,684/28, numerators are 35,16,684
Denominators are 96,64,28
The GCF of 35,16,684 is 1 .
LCM of 96,64,28 is 1344.
The greatest common factor of 35/96,16/64,684/28 = [GCF of 35,16,684]/[LCM of 96,64,28]= 1/1344
Therefore, the GCF of 35/96,16/64,684/28 is 1/1344.
To find the highest common factor of 35,16,684, we have to find the factors of both numbers and list the highest common factor.
The factors of 35 are 1, 5, 7, 35
The factors of 16 are 1, 2, 4, 8, 16
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The HCF of 35,16,684 is 1.
Lets's calculate GCF of 35,16,684
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 35,16,684 By Matching Biggest Common Factor Method
Now, list down the factors of 35
:1,5,7,35
Now, list down the factors of 16
:1,2,4,8,16
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Greatest Common Factor
We found the factors 35,16,684 . The biggest common factor number is the GCF number.
So the greatest common factor 35,16,684 is 1.
Lets's calculate LCM of 96,64,28
| 2 | 96, 64, 28 |
| 2 | 48, 32, 14 |
| 2 | 24, 16, 7 |
| 2 | 12, 8, 7 |
| 2 | 6, 4, 7 |
| 3, 2, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 3 x 2 x 7 = 1344
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1344
Therefore, the GCF of Fractions 35/96,16/64,684/28 is 1/1344
Least Common Multiple of 96,64,28 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 96,64,28 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(96,64,28) = 4
common factors(in case of two or more numbers have common factors) = 32
GCF(96,64,28) x common factors =4 x 32 = 128
LCM(96,64,28) = ( 96 × 64 × 28 ) / 128
LCM(96,64,28) = 172032 / 128
LCM(96,64,28) = 1344
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FAQs on GCF of Fractions of 35/96, 16/64, 684/28
1. What is the HCF of 35,16,684?
The HCF of 35,16,684 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 35/96, 16/64, 684/28?
Answer: GCF of Numerators as per given numbers 35/96, 16/64, 684/28 is
GCF of Numerators i.e. for 35,16,684 is 1
LCM of denominators i.e. for 96,64,28 is 1344.
Thus, GCF of Fractions is 1/1344.Finally, GCF of Fractions for 35/96, 16/64, 684/28 is 1/1344.