GCF of 8672/103, 7712/3413
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8672/103, 7712/3413 i.e 32/351539 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8672/103, 7712/3413.
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 8672/103,7712/3413?
Given fractions are 8672/103,7712/3413
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 8672/103,7712/3413, numerators are 8672,7712
Denominators are 103,3413
The GCF of 8672,7712 is 32 .
LCM of 103,3413 is 351539.
The greatest common factor of 8672/103,7712/3413 = [GCF of 8672,7712]/[LCM of 103,3413]= 32/351539
Therefore, the GCF of 8672/103,7712/3413 is 32/351539.
To find the highest common factor of 8672,7712, we have to find the factors of both numbers and list the highest common factor.
The factors of 8672 are 1, 2, 4, 8, 16, 32, 271, 542, 1084, 2168, 4336, 8672
The factors of 7712 are 1, 2, 4, 8, 16, 32, 241, 482, 964, 1928, 3856, 7712
The HCF of 8672,7712 is 32.
Lets's calculate GCF of 8672,7712
| 2 | 8672, 7712 |
| 2 | 4336, 3856 |
| 2 | 2168, 1928 |
| 2 | 1084, 964 |
| 2 | 542, 482 |
| 271, 241 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32
Greatest Common Factor of 8672,7712 By Matching Biggest Common Factor Method
Now, list down the factors of 8672
:1,2,4,8,16,32,271,542,1084,2168,4336,8672
Now, list down the factors of 7712
:1,2,4,8,16,32,241,482,964,1928,3856,7712
Greatest Common Factor
We found the factors 8672,7712 . The biggest common factor number is the GCF number.
So the greatest common factor 8672,7712 is 32.
Lets's calculate LCM of 103,3413
Given numbers has no common factors except 1. So, there LCM is their product i.e 351539
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/351539
Therefore, the GCF of Fractions 8672/103,7712/3413 is 32/351539
Least Common Multiple of 103,3413 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 103,3413 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(103,3413) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(103,3413) x common factors =1 x 1 = 1
LCM(103,3413) = ( 103 × 3413 ) / 1
LCM(103,3413) = 351539 / 1
LCM(103,3413) = 351539
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FAQs on GCF of Fractions of 8672/103, 7712/3413
1. What is the HCF of 8672,7712?
The HCF of 8672,7712 is 32
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 8672/103, 7712/3413?
Answer: GCF of Numerators as per given numbers 8672/103, 7712/3413 is
GCF of Numerators i.e. for 8672,7712 is 32
LCM of denominators i.e. for 103,3413 is 351539.
Thus, GCF of Fractions is 32/351539.Finally, GCF of Fractions for 8672/103, 7712/3413 is 32/351539.