GCF of 7312/824, 9036/5678
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7312/824, 9036/5678 i.e 4/2339336 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7312/824, 9036/5678.
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 7312/824,9036/5678?
Given fractions are 7312/824,9036/5678
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 7312/824,9036/5678, numerators are 7312,9036
Denominators are 824,5678
The GCF of 7312,9036 is 4 .
LCM of 824,5678 is 2339336.
The greatest common factor of 7312/824,9036/5678 = [GCF of 7312,9036]/[LCM of 824,5678]= 4/2339336
Therefore, the GCF of 7312/824,9036/5678 is 4/2339336.
To find the highest common factor of 7312,9036, we have to find the factors of both numbers and list the highest common factor.
The factors of 7312 are 1, 2, 4, 8, 16, 457, 914, 1828, 3656, 7312
The factors of 9036 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 251, 502, 753, 1004, 1506, 2259, 3012, 4518, 9036
The HCF of 7312,9036 is 4.
Lets's calculate GCF of 7312,9036
| 2 | 7312, 9036 |
| 2 | 3656, 4518 |
| 1828, 2259 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 7312,9036 By Matching Biggest Common Factor Method
Now, list down the factors of 7312
:1,2,4,8,16,457,914,1828,3656,7312
Now, list down the factors of 9036
:1,2,3,4,6,9,12,18,36,251,502,753,1004,1506,2259,3012,4518,9036
Greatest Common Factor
We found the factors 7312,9036 . The biggest common factor number is the GCF number.
So the greatest common factor 7312,9036 is 4.
Lets's calculate LCM of 824,5678
| 2 | 824, 5678 |
| 412, 2839 |
∴ So the LCM of the given numbers is 2 x 412 x 2839 = 2339336
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/2339336
Therefore, the GCF of Fractions 7312/824,9036/5678 is 4/2339336
Least Common Multiple of 824,5678 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 824,5678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(824,5678) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(824,5678) x common factors =2 x 1 = 2
LCM(824,5678) = ( 824 × 5678 ) / 2
LCM(824,5678) = 4678672 / 2
LCM(824,5678) = 2339336
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FAQs on GCF of Fractions of 7312/824, 9036/5678
1. What is the HCF of 7312,9036?
The HCF of 7312,9036 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 7312/824, 9036/5678?
Answer: GCF of Numerators as per given numbers 7312/824, 9036/5678 is
GCF of Numerators i.e. for 7312,9036 is 4
LCM of denominators i.e. for 824,5678 is 2339336.
Thus, GCF of Fractions is 4/2339336.Finally, GCF of Fractions for 7312/824, 9036/5678 is 4/2339336.