Use our free GCF of Fractions Calculator tool to compute the GCF of 462/247, 748/429 i.e 22/8151 easily. The following is the detailed procedure to determine the greatest common factor of fractions 462/247, 748/429.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 462/247,748/429
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 462/247,748/429, numerators are 462,748
Denominators are 247,429
The GCF of 462,748 is 22 .
LCM of 247,429 is 8151.
The greatest common factor of 462/247,748/429 = [GCF of 462,748]/[LCM of 247,429]= 22/8151
Therefore, the GCF of 462/247,748/429 is 22/8151.
To find the highest common factor of 462,748, we have to find the factors of both numbers and list the highest common factor.
The factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462
The factors of 748 are 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748
The HCF of 462,748 is 22.
Lets's calculate GCF of 462,748
2 | 462, 748 |
11 | 231, 374 |
21, 34 |
∴ So the GCF of the given numbers is 2 x 11 = 22
Now, list down the factors of 462
:1,2,3,6,7,11,14,21,22,33,42,66,77,154,231,462
Now, list down the factors of 748
:1,2,4,11,17,22,34,44,68,187,374,748
Greatest Common Factor
We found the factors 462,748 . The biggest common factor number is the GCF number.
So the greatest common factor 462,748 is 22.
Lets's calculate LCM of 247,429
13 | 247, 429 |
19, 33 |
∴ So the LCM of the given numbers is 13 x 19 x 33 = 8151
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/8151
Therefore, the GCF of Fractions 462/247,748/429 is 22/8151
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 247,429 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(247,429) = 13
common factors(in case of two or more numbers have common factors) = 1
GCF(247,429) x common factors =13 x 1 = 13
LCM(247,429) = ( 247 × 429 ) / 13
LCM(247,429) = 105963 / 13
LCM(247,429) = 8151
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 462,748?
The HCF of 462,748 is 22
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 462/247, 748/429?
Answer: GCF of Numerators as per given numbers 462/247, 748/429 is
GCF of Numerators i.e. for 462,748 is 22
LCM of denominators i.e. for 247,429 is 8151.
Thus, GCF of Fractions is 22/8151.Finally, GCF of Fractions for 462/247, 748/429 is 22/8151.