GCF of 302/75, 972/48, 682/64
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 302/75, 972/48, 682/64 i.e 2/4800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 302/75, 972/48, 682/64.
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 302/75,972/48,682/64?
Given fractions are 302/75,972/48,682/64
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 302/75,972/48,682/64, numerators are 302,972,682
Denominators are 75,48,64
The GCF of 302,972,682 is 2 .
LCM of 75,48,64 is 4800.
The greatest common factor of 302/75,972/48,682/64 = [GCF of 302,972,682]/[LCM of 75,48,64]= 2/4800
Therefore, the GCF of 302/75,972/48,682/64 is 2/4800.
To find the highest common factor of 302,972,682, we have to find the factors of both numbers and list the highest common factor.
The factors of 302 are 1, 2, 151, 302
The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
The factors of 682 are 1, 2, 11, 22, 31, 62, 341, 682
The HCF of 302,972,682 is 2.
Lets's calculate GCF of 302,972,682
| 2 | 302, 972, 682 |
| 151, 486, 341 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 302,972,682 By Matching Biggest Common Factor Method
Now, list down the factors of 302
:1,2,151,302
Now, list down the factors of 972
:1,2,3,4,6,9,12,18,27,36,54,81,108,162,243,324,486,972
Now, list down the factors of 682
:1,2,11,22,31,62,341,682
Greatest Common Factor
We found the factors 302,972,682 . The biggest common factor number is the GCF number.
So the greatest common factor 302,972,682 is 2.
Lets's calculate LCM of 75,48,64
| 2 | 75, 48, 64 |
| 2 | 75, 24, 32 |
| 2 | 75, 12, 16 |
| 2 | 75, 6, 8 |
| 3 | 75, 3, 4 |
| 25, 1, 4 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 3 x 25 x 1 x 4 = 4800
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/4800
Therefore, the GCF of Fractions 302/75,972/48,682/64 is 2/4800
Least Common Multiple of 75,48,64 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 75,48,64 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,48,64) = 1
common factors(in case of two or more numbers have common factors) = 48
GCF(75,48,64) x common factors =1 x 48 = 48
LCM(75,48,64) = ( 75 × 48 × 64 ) / 48
LCM(75,48,64) = 230400 / 48
LCM(75,48,64) = 4800
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FAQs on GCF of Fractions of 302/75, 972/48, 682/64
1. What is the HCF of 302,972,682?
The HCF of 302,972,682 is 2
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 302/75, 972/48, 682/64?
Answer: GCF of Numerators as per given numbers 302/75, 972/48, 682/64 is
GCF of Numerators i.e. for 302,972,682 is 2
LCM of denominators i.e. for 75,48,64 is 4800.
Thus, GCF of Fractions is 2/4800.Finally, GCF of Fractions for 302/75, 972/48, 682/64 is 2/4800.