GCF of 168/722, 960/982
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 168/722, 960/982 i.e 24/354502 easily. The following is the detailed procedure to determine the greatest common factor of fractions 168/722, 960/982.
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 168/722,960/982?
Given fractions are 168/722,960/982
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 168/722,960/982, numerators are 168,960
Denominators are 722,982
The GCF of 168,960 is 24 .
LCM of 722,982 is 354502.
The greatest common factor of 168/722,960/982 = [GCF of 168,960]/[LCM of 722,982]= 24/354502
Therefore, the GCF of 168/722,960/982 is 24/354502.
To find the highest common factor of 168,960, we have to find the factors of both numbers and list the highest common factor.
The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
The factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
The HCF of 168,960 is 24.
Lets's calculate GCF of 168,960
| 2 | 168, 960 |
| 2 | 84, 480 |
| 2 | 42, 240 |
| 3 | 21, 120 |
| 7, 40 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24
Greatest Common Factor of 168,960 By Matching Biggest Common Factor Method
Now, list down the factors of 168
:1,2,3,4,6,7,8,12,14,21,24,28,42,56,84,168
Now, list down the factors of 960
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,64,80,96,120,160,192,240,320,480,960
Greatest Common Factor
We found the factors 168,960 . The biggest common factor number is the GCF number.
So the greatest common factor 168,960 is 24.
Lets's calculate LCM of 722,982
| 2 | 722, 982 |
| 361, 491 |
∴ So the LCM of the given numbers is 2 x 361 x 491 = 354502
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/354502
Therefore, the GCF of Fractions 168/722,960/982 is 24/354502
Least Common Multiple of 722,982 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 722,982 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(722,982) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(722,982) x common factors =2 x 1 = 2
LCM(722,982) = ( 722 × 982 ) / 2
LCM(722,982) = 709004 / 2
LCM(722,982) = 354502
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FAQs on GCF of Fractions of 168/722, 960/982
1. What is the HCF of 168,960?
The HCF of 168,960 is 24
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 168/722, 960/982?
Answer: GCF of Numerators as per given numbers 168/722, 960/982 is
GCF of Numerators i.e. for 168,960 is 24
LCM of denominators i.e. for 722,982 is 354502.
Thus, GCF of Fractions is 24/354502.Finally, GCF of Fractions for 168/722, 960/982 is 24/354502.