GCF of 7712/492, 8404/916
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7712/492, 8404/916 i.e 4/112668 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7712/492, 8404/916.
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 7712/492,8404/916?
Given fractions are 7712/492,8404/916
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 7712/492,8404/916, numerators are 7712,8404
Denominators are 492,916
The GCF of 7712,8404 is 4 .
LCM of 492,916 is 112668.
The greatest common factor of 7712/492,8404/916 = [GCF of 7712,8404]/[LCM of 492,916]= 4/112668
Therefore, the GCF of 7712/492,8404/916 is 4/112668.
To find the highest common factor of 7712,8404, 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 8404 are 1, 2, 4, 11, 22, 44, 191, 382, 764, 2101, 4202, 8404
The HCF of 7712,8404 is 4.
Lets's calculate GCF of 7712,8404
| 2 | 7712, 8404 |
| 2 | 3856, 4202 |
| 1928, 2101 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 7712,8404 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 8404
:1,2,4,11,22,44,191,382,764,2101,4202,8404
Greatest Common Factor
We found the factors 7712,8404 . The biggest common factor number is the GCF number.
So the greatest common factor 7712,8404 is 4.
Lets's calculate LCM of 492,916
| 2 | 492, 916 |
| 2 | 246, 458 |
| 123, 229 |
∴ So the LCM of the given numbers is 2 x 2 x 123 x 229 = 112668
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/112668
Therefore, the GCF of Fractions 7712/492,8404/916 is 4/112668
Least Common Multiple of 492,916 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 492,916 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(492,916) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(492,916) x common factors =4 x 1 = 4
LCM(492,916) = ( 492 × 916 ) / 4
LCM(492,916) = 450672 / 4
LCM(492,916) = 112668
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FAQs on GCF of Fractions of 7712/492, 8404/916
1. What is the HCF of 7712,8404?
The HCF of 7712,8404 is 4
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 7712/492, 8404/916?
Answer: GCF of Numerators as per given numbers 7712/492, 8404/916 is
GCF of Numerators i.e. for 7712,8404 is 4
LCM of denominators i.e. for 492,916 is 112668.
Thus, GCF of Fractions is 4/112668.Finally, GCF of Fractions for 7712/492, 8404/916 is 4/112668.