GCF of 408/96, 722/6750
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 408/96, 722/6750 i.e 2/108000 easily. The following is the detailed procedure to determine the greatest common factor of fractions 408/96, 722/6750.
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 408/96,722/6750?
Given fractions are 408/96,722/6750
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 408/96,722/6750, numerators are 408,722
Denominators are 96,6750
The GCF of 408,722 is 2 .
LCM of 96,6750 is 108000.
The greatest common factor of 408/96,722/6750 = [GCF of 408,722]/[LCM of 96,6750]= 2/108000
Therefore, the GCF of 408/96,722/6750 is 2/108000.
To find the highest common factor of 408,722, we have to find the factors of both numbers and list the highest common factor.
The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
The factors of 722 are 1, 2, 19, 38, 361, 722
The HCF of 408,722 is 2.
Lets's calculate GCF of 408,722
| 2 | 408, 722 |
| 204, 361 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 408,722 By Matching Biggest Common Factor Method
Now, list down the factors of 408
:1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408
Now, list down the factors of 722
:1,2,19,38,361,722
Greatest Common Factor
We found the factors 408,722 . The biggest common factor number is the GCF number.
So the greatest common factor 408,722 is 2.
Lets's calculate LCM of 96,6750
| 2 | 96, 6750 |
| 3 | 48, 3375 |
| 16, 1125 |
∴ So the LCM of the given numbers is 2 x 3 x 16 x 1125 = 108000
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/108000
Therefore, the GCF of Fractions 408/96,722/6750 is 2/108000
Least Common Multiple of 96,6750 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 96,6750 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(96,6750) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(96,6750) x common factors =6 x 1 = 6
LCM(96,6750) = ( 96 × 6750 ) / 6
LCM(96,6750) = 648000 / 6
LCM(96,6750) = 108000
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FAQs on GCF of Fractions of 408/96, 722/6750
1. What is the HCF of 408,722?
The HCF of 408,722 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 408/96, 722/6750?
Answer: GCF of Numerators as per given numbers 408/96, 722/6750 is
GCF of Numerators i.e. for 408,722 is 2
LCM of denominators i.e. for 96,6750 is 108000.
Thus, GCF of Fractions is 2/108000.Finally, GCF of Fractions for 408/96, 722/6750 is 2/108000.