GCF of 684/72, 408/689
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 684/72, 408/689 i.e 12/49608 easily. The following is the detailed procedure to determine the greatest common factor of fractions 684/72, 408/689.
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 684/72,408/689?
Given fractions are 684/72,408/689
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 684/72,408/689, numerators are 684,408
Denominators are 72,689
The GCF of 684,408 is 12 .
LCM of 72,689 is 49608.
The greatest common factor of 684/72,408/689 = [GCF of 684,408]/[LCM of 72,689]= 12/49608
Therefore, the GCF of 684/72,408/689 is 12/49608.
To find the highest common factor of 684,408, we have to find the factors of both numbers and list the highest common factor.
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
The HCF of 684,408 is 12.
Lets's calculate GCF of 684,408
| 2 | 684, 408 |
| 2 | 342, 204 |
| 3 | 171, 102 |
| 57, 34 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 684,408 By Matching Biggest Common Factor Method
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Now, list down the factors of 408
:1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408
Greatest Common Factor
We found the factors 684,408 . The biggest common factor number is the GCF number.
So the greatest common factor 684,408 is 12.
Lets's calculate LCM of 72,689
Given numbers has no common factors except 1. So, there LCM is their product i.e 49608
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/49608
Therefore, the GCF of Fractions 684/72,408/689 is 12/49608
Least Common Multiple of 72,689 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 72,689 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(72,689) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(72,689) x common factors =1 x 1 = 1
LCM(72,689) = ( 72 × 689 ) / 1
LCM(72,689) = 49608 / 1
LCM(72,689) = 49608
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FAQs on GCF of Fractions of 684/72, 408/689
1. What is the HCF of 684,408?
The HCF of 684,408 is 12
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 684/72, 408/689?
Answer: GCF of Numerators as per given numbers 684/72, 408/689 is
GCF of Numerators i.e. for 684,408 is 12
LCM of denominators i.e. for 72,689 is 49608.
Thus, GCF of Fractions is 12/49608.Finally, GCF of Fractions for 684/72, 408/689 is 12/49608.