GCF of 7712/897, 7424/578
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7712/897, 7424/578 i.e 32/518466 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7712/897, 7424/578.
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 7712/897,7424/578?
Given fractions are 7712/897,7424/578
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 7712/897,7424/578, numerators are 7712,7424
Denominators are 897,578
The GCF of 7712,7424 is 32 .
LCM of 897,578 is 518466.
The greatest common factor of 7712/897,7424/578 = [GCF of 7712,7424]/[LCM of 897,578]= 32/518466
Therefore, the GCF of 7712/897,7424/578 is 32/518466.
To find the highest common factor of 7712,7424, we have to find the factors of both numbers and list the highest common factor.
The factors of 7712 are 1, 2, 4, 8, 16, 32, 241, 482, 964, 1928, 3856, 7712
The factors of 7424 are 1, 2, 4, 8, 16, 29, 32, 58, 64, 116, 128, 232, 256, 464, 928, 1856, 3712, 7424
The HCF of 7712,7424 is 32.
Lets's calculate GCF of 7712,7424
| 2 | 7712, 7424 |
| 2 | 3856, 3712 |
| 2 | 1928, 1856 |
| 2 | 964, 928 |
| 2 | 482, 464 |
| 241, 232 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32
Greatest Common Factor of 7712,7424 By Matching Biggest Common Factor Method
Now, list down the factors of 7712
:1,2,4,8,16,32,241,482,964,1928,3856,7712
Now, list down the factors of 7424
:1,2,4,8,16,29,32,58,64,116,128,232,256,464,928,1856,3712,7424
Greatest Common Factor
We found the factors 7712,7424 . The biggest common factor number is the GCF number.
So the greatest common factor 7712,7424 is 32.
Lets's calculate LCM of 897,578
Given numbers has no common factors except 1. So, there LCM is their product i.e 518466
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/518466
Therefore, the GCF of Fractions 7712/897,7424/578 is 32/518466
Least Common Multiple of 897,578 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 897,578 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(897,578) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(897,578) x common factors =1 x 1 = 1
LCM(897,578) = ( 897 × 578 ) / 1
LCM(897,578) = 518466 / 1
LCM(897,578) = 518466
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FAQs on GCF of Fractions of 7712/897, 7424/578
1. What is the HCF of 7712,7424?
The HCF of 7712,7424 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 7712/897, 7424/578?
Answer: GCF of Numerators as per given numbers 7712/897, 7424/578 is
GCF of Numerators i.e. for 7712,7424 is 32
LCM of denominators i.e. for 897,578 is 518466.
Thus, GCF of Fractions is 32/518466.Finally, GCF of Fractions for 7712/897, 7424/578 is 32/518466.