GCF of 767/578, 322/458
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 767/578, 322/458 i.e 1/132362 easily. The following is the detailed procedure to determine the greatest common factor of fractions 767/578, 322/458.
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 767/578,322/458?
Given fractions are 767/578,322/458
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 767/578,322/458, numerators are 767,322
Denominators are 578,458
The GCF of 767,322 is 1 .
LCM of 578,458 is 132362.
The greatest common factor of 767/578,322/458 = [GCF of 767,322]/[LCM of 578,458]= 1/132362
Therefore, the GCF of 767/578,322/458 is 1/132362.
To find the highest common factor of 767,322, we have to find the factors of both numbers and list the highest common factor.
The factors of 767 are 1, 13, 59, 767
The factors of 322 are 1, 2, 7, 14, 23, 46, 161, 322
The HCF of 767,322 is 1.
Lets's calculate GCF of 767,322
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 767,322 By Matching Biggest Common Factor Method
Now, list down the factors of 767
:1,13,59,767
Now, list down the factors of 322
:1,2,7,14,23,46,161,322
Greatest Common Factor
We found the factors 767,322 . The biggest common factor number is the GCF number.
So the greatest common factor 767,322 is 1.
Lets's calculate LCM of 578,458
| 2 | 578, 458 |
| 289, 229 |
∴ So the LCM of the given numbers is 2 x 289 x 229 = 132362
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/132362
Therefore, the GCF of Fractions 767/578,322/458 is 1/132362
Least Common Multiple of 578,458 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 578,458 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(578,458) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(578,458) x common factors =2 x 1 = 2
LCM(578,458) = ( 578 × 458 ) / 2
LCM(578,458) = 264724 / 2
LCM(578,458) = 132362
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FAQs on GCF of Fractions of 767/578, 322/458
1. What is the HCF of 767,322?
The HCF of 767,322 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 767/578, 322/458?
Answer: GCF of Numerators as per given numbers 767/578, 322/458 is
GCF of Numerators i.e. for 767,322 is 1
LCM of denominators i.e. for 578,458 is 132362.
Thus, GCF of Fractions is 1/132362.Finally, GCF of Fractions for 767/578, 322/458 is 1/132362.