GCF of 4664/274, 5724/1692
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4664/274, 5724/1692 i.e 212/231804 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4664/274, 5724/1692.
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 4664/274,5724/1692?
Given fractions are 4664/274,5724/1692
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 4664/274,5724/1692, numerators are 4664,5724
Denominators are 274,1692
The GCF of 4664,5724 is 212 .
LCM of 274,1692 is 231804.
The greatest common factor of 4664/274,5724/1692 = [GCF of 4664,5724]/[LCM of 274,1692]= 212/231804
Therefore, the GCF of 4664/274,5724/1692 is 212/231804.
To find the highest common factor of 4664,5724, we have to find the factors of both numbers and list the highest common factor.
The factors of 4664 are 1, 2, 4, 8, 11, 22, 44, 53, 88, 106, 212, 424, 583, 1166, 2332, 4664
The factors of 5724 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 53, 54, 106, 108, 159, 212, 318, 477, 636, 954, 1431, 1908, 2862, 5724
The HCF of 4664,5724 is 212.
Lets's calculate GCF of 4664,5724
| 2 | 4664, 5724 |
| 2 | 2332, 2862 |
| 53 | 1166, 1431 |
| 22, 27 |
∴ So the GCF of the given numbers is 2 x 2 x 53 = 212
Greatest Common Factor of 4664,5724 By Matching Biggest Common Factor Method
Now, list down the factors of 4664
:1,2,4,8,11,22,44,53,88,106,212,424,583,1166,2332,4664
Now, list down the factors of 5724
:1,2,3,4,6,9,12,18,27,36,53,54,106,108,159,212,318,477,636,954,1431,1908,2862,5724
Greatest Common Factor
We found the factors 4664,5724 . The biggest common factor number is the GCF number.
So the greatest common factor 4664,5724 is 212.
Lets's calculate LCM of 274,1692
| 2 | 274, 1692 |
| 137, 846 |
∴ So the LCM of the given numbers is 2 x 137 x 846 = 231804
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 212/231804
Therefore, the GCF of Fractions 4664/274,5724/1692 is 212/231804
Least Common Multiple of 274,1692 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 274,1692 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(274,1692) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(274,1692) x common factors =2 x 1 = 2
LCM(274,1692) = ( 274 × 1692 ) / 2
LCM(274,1692) = 463608 / 2
LCM(274,1692) = 231804
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FAQs on GCF of Fractions of 4664/274, 5724/1692
1. What is the HCF of 4664,5724?
The HCF of 4664,5724 is 212
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 4664/274, 5724/1692?
Answer: GCF of Numerators as per given numbers 4664/274, 5724/1692 is
GCF of Numerators i.e. for 4664,5724 is 212
LCM of denominators i.e. for 274,1692 is 231804.
Thus, GCF of Fractions is 212/231804.Finally, GCF of Fractions for 4664/274, 5724/1692 is 212/231804.