GCF of 782/342, 322/728
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 782/342, 322/728 i.e 46/124488 easily. The following is the detailed procedure to determine the greatest common factor of fractions 782/342, 322/728.
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 782/342,322/728?
Given fractions are 782/342,322/728
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 782/342,322/728, numerators are 782,322
Denominators are 342,728
The GCF of 782,322 is 46 .
LCM of 342,728 is 124488.
The greatest common factor of 782/342,322/728 = [GCF of 782,322]/[LCM of 342,728]= 46/124488
Therefore, the GCF of 782/342,322/728 is 46/124488.
To find the highest common factor of 782,322, we have to find the factors of both numbers and list the highest common factor.
The factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782
The factors of 322 are 1, 2, 7, 14, 23, 46, 161, 322
The HCF of 782,322 is 46.
Lets's calculate GCF of 782,322
| 2 | 782, 322 |
| 23 | 391, 161 |
| 17, 7 |
∴ So the GCF of the given numbers is 2 x 23 = 46
Greatest Common Factor of 782,322 By Matching Biggest Common Factor Method
Now, list down the factors of 782
:1,2,17,23,34,46,391,782
Now, list down the factors of 322
:1,2,7,14,23,46,161,322
Greatest Common Factor
We found the factors 782,322 . The biggest common factor number is the GCF number.
So the greatest common factor 782,322 is 46.
Lets's calculate LCM of 342,728
| 2 | 342, 728 |
| 171, 364 |
∴ So the LCM of the given numbers is 2 x 171 x 364 = 124488
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 46/124488
Therefore, the GCF of Fractions 782/342,322/728 is 46/124488
Least Common Multiple of 342,728 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 342,728 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(342,728) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(342,728) x common factors =2 x 1 = 2
LCM(342,728) = ( 342 × 728 ) / 2
LCM(342,728) = 248976 / 2
LCM(342,728) = 124488
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FAQs on GCF of Fractions of 782/342, 322/728
1. What is the HCF of 782,322?
The HCF of 782,322 is 46
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 782/342, 322/728?
Answer: GCF of Numerators as per given numbers 782/342, 322/728 is
GCF of Numerators i.e. for 782,322 is 46
LCM of denominators i.e. for 342,728 is 124488.
Thus, GCF of Fractions is 46/124488.Finally, GCF of Fractions for 782/342, 322/728 is 46/124488.