GCF of 5984/106, 3792/3682
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5984/106, 3792/3682 i.e 16/195146 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5984/106, 3792/3682.
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 5984/106,3792/3682?
Given fractions are 5984/106,3792/3682
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 5984/106,3792/3682, numerators are 5984,3792
Denominators are 106,3682
The GCF of 5984,3792 is 16 .
LCM of 106,3682 is 195146.
The greatest common factor of 5984/106,3792/3682 = [GCF of 5984,3792]/[LCM of 106,3682]= 16/195146
Therefore, the GCF of 5984/106,3792/3682 is 16/195146.
To find the highest common factor of 5984,3792, we have to find the factors of both numbers and list the highest common factor.
The factors of 5984 are 1, 2, 4, 8, 11, 16, 17, 22, 32, 34, 44, 68, 88, 136, 176, 187, 272, 352, 374, 544, 748, 1496, 2992, 5984
The factors of 3792 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 79, 158, 237, 316, 474, 632, 948, 1264, 1896, 3792
The HCF of 5984,3792 is 16.
Lets's calculate GCF of 5984,3792
| 2 | 5984, 3792 |
| 2 | 2992, 1896 |
| 2 | 1496, 948 |
| 2 | 748, 474 |
| 374, 237 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Greatest Common Factor of 5984,3792 By Matching Biggest Common Factor Method
Now, list down the factors of 5984
:1,2,4,8,11,16,17,22,32,34,44,68,88,136,176,187,272,352,374,544,748,1496,2992,5984
Now, list down the factors of 3792
:1,2,3,4,6,8,12,16,24,48,79,158,237,316,474,632,948,1264,1896,3792
Greatest Common Factor
We found the factors 5984,3792 . The biggest common factor number is the GCF number.
So the greatest common factor 5984,3792 is 16.
Lets's calculate LCM of 106,3682
| 2 | 106, 3682 |
| 53, 1841 |
∴ So the LCM of the given numbers is 2 x 53 x 1841 = 195146
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/195146
Therefore, the GCF of Fractions 5984/106,3792/3682 is 16/195146
Least Common Multiple of 106,3682 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 106,3682 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(106,3682) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(106,3682) x common factors =2 x 1 = 2
LCM(106,3682) = ( 106 × 3682 ) / 2
LCM(106,3682) = 390292 / 2
LCM(106,3682) = 195146
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FAQs on GCF of Fractions of 5984/106, 3792/3682
1. What is the HCF of 5984,3792?
The HCF of 5984,3792 is 16
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 5984/106, 3792/3682?
Answer: GCF of Numerators as per given numbers 5984/106, 3792/3682 is
GCF of Numerators i.e. for 5984,3792 is 16
LCM of denominators i.e. for 106,3682 is 195146.
Thus, GCF of Fractions is 16/195146.Finally, GCF of Fractions for 5984/106, 3792/3682 is 16/195146.