GCF of 474/637, 678/258
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 474/637, 678/258 i.e 6/164346 easily. The following is the detailed procedure to determine the greatest common factor of fractions 474/637, 678/258.
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 474/637,678/258?
Given fractions are 474/637,678/258
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 474/637,678/258, numerators are 474,678
Denominators are 637,258
The GCF of 474,678 is 6 .
LCM of 637,258 is 164346.
The greatest common factor of 474/637,678/258 = [GCF of 474,678]/[LCM of 637,258]= 6/164346
Therefore, the GCF of 474/637,678/258 is 6/164346.
To find the highest common factor of 474,678, we have to find the factors of both numbers and list the highest common factor.
The factors of 474 are 1, 2, 3, 6, 79, 158, 237, 474
The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678
The HCF of 474,678 is 6.
Lets's calculate GCF of 474,678
| 2 | 474, 678 |
| 3 | 237, 339 |
| 79, 113 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 474,678 By Matching Biggest Common Factor Method
Now, list down the factors of 474
:1,2,3,6,79,158,237,474
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Greatest Common Factor
We found the factors 474,678 . The biggest common factor number is the GCF number.
So the greatest common factor 474,678 is 6.
Lets's calculate LCM of 637,258
Given numbers has no common factors except 1. So, there LCM is their product i.e 164346
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/164346
Therefore, the GCF of Fractions 474/637,678/258 is 6/164346
Least Common Multiple of 637,258 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 637,258 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(637,258) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(637,258) x common factors =1 x 1 = 1
LCM(637,258) = ( 637 × 258 ) / 1
LCM(637,258) = 164346 / 1
LCM(637,258) = 164346
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FAQs on GCF of Fractions of 474/637, 678/258
1. What is the HCF of 474,678?
The HCF of 474,678 is 6
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 474/637, 678/258?
Answer: GCF of Numerators as per given numbers 474/637, 678/258 is
GCF of Numerators i.e. for 474,678 is 6
LCM of denominators i.e. for 637,258 is 164346.
Thus, GCF of Fractions is 6/164346.Finally, GCF of Fractions for 474/637, 678/258 is 6/164346.