Use our free GCF of Fractions Calculator tool to compute the GCF of 924/972, 231/840 i.e 231/68040 easily. The following is the detailed procedure to determine the greatest common factor of fractions 924/972, 231/840.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 924/972,231/840
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 924/972,231/840, numerators are 924,231
Denominators are 972,840
The GCF of 924,231 is 231 .
LCM of 972,840 is 68040.
The greatest common factor of 924/972,231/840 = [GCF of 924,231]/[LCM of 972,840]= 231/68040
Therefore, the GCF of 924/972,231/840 is 231/68040.
To find the highest common factor of 924,231, we have to find the factors of both numbers and list the highest common factor.
The factors of 924 are 1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462, 924
The factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231
The HCF of 924,231 is 231.
Lets's calculate GCF of 924,231
3 | 924, 231 |
7 | 308, 77 |
11 | 44, 11 |
4, 1 |
∴ So the GCF of the given numbers is 3 x 7 x 11 = 231
Now, list down the factors of 924
:1,2,3,4,6,7,11,12,14,21,22,28,33,42,44,66,77,84,132,154,231,308,462,924
Now, list down the factors of 231
:1,3,7,11,21,33,77,231
Greatest Common Factor
We found the factors 924,231 . The biggest common factor number is the GCF number.
So the greatest common factor 924,231 is 231.
Lets's calculate LCM of 972,840
2 | 972, 840 |
2 | 486, 420 |
3 | 243, 210 |
81, 70 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 81 x 70 = 68040
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 231/68040
Therefore, the GCF of Fractions 924/972,231/840 is 231/68040
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 972,840 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(972,840) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(972,840) x common factors =12 x 1 = 12
LCM(972,840) = ( 972 × 840 ) / 12
LCM(972,840) = 816480 / 12
LCM(972,840) = 68040
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 924,231?
The HCF of 924,231 is 231
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 924/972, 231/840?
Answer: GCF of Numerators as per given numbers 924/972, 231/840 is
GCF of Numerators i.e. for 924,231 is 231
LCM of denominators i.e. for 972,840 is 68040.
Thus, GCF of Fractions is 231/68040.Finally, GCF of Fractions for 924/972, 231/840 is 231/68040.