GCF of 7182/472, 8574/8000
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7182/472, 8574/8000 i.e 6/472000 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7182/472, 8574/8000.
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 7182/472,8574/8000?
Given fractions are 7182/472,8574/8000
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 7182/472,8574/8000, numerators are 7182,8574
Denominators are 472,8000
The GCF of 7182,8574 is 6 .
LCM of 472,8000 is 472000.
The greatest common factor of 7182/472,8574/8000 = [GCF of 7182,8574]/[LCM of 472,8000]= 6/472000
Therefore, the GCF of 7182/472,8574/8000 is 6/472000.
To find the highest common factor of 7182,8574, we have to find the factors of both numbers and list the highest common factor.
The factors of 7182 are 1, 2, 3, 6, 7, 9, 14, 18, 19, 21, 27, 38, 42, 54, 57, 63, 114, 126, 133, 171, 189, 266, 342, 378, 399, 513, 798, 1026, 1197, 2394, 3591, 7182
The factors of 8574 are 1, 2, 3, 6, 1429, 2858, 4287, 8574
The HCF of 7182,8574 is 6.
Lets's calculate GCF of 7182,8574
| 2 | 7182, 8574 |
| 3 | 3591, 4287 |
| 1197, 1429 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 7182,8574 By Matching Biggest Common Factor Method
Now, list down the factors of 7182
:1,2,3,6,7,9,14,18,19,21,27,38,42,54,57,63,114,126,133,171,189,266,342,378,399,513,798,1026,1197,2394,3591,7182
Now, list down the factors of 8574
:1,2,3,6,1429,2858,4287,8574
Greatest Common Factor
We found the factors 7182,8574 . The biggest common factor number is the GCF number.
So the greatest common factor 7182,8574 is 6.
Lets's calculate LCM of 472,8000
| 2 | 472, 8000 |
| 2 | 236, 4000 |
| 2 | 118, 2000 |
| 59, 1000 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 59 x 1000 = 472000
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/472000
Therefore, the GCF of Fractions 7182/472,8574/8000 is 6/472000
Least Common Multiple of 472,8000 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 472,8000 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(472,8000) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(472,8000) x common factors =8 x 1 = 8
LCM(472,8000) = ( 472 × 8000 ) / 8
LCM(472,8000) = 3776000 / 8
LCM(472,8000) = 472000
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FAQs on GCF of Fractions of 7182/472, 8574/8000
1. What is the HCF of 7182,8574?
The HCF of 7182,8574 is 6
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 7182/472, 8574/8000?
Answer: GCF of Numerators as per given numbers 7182/472, 8574/8000 is
GCF of Numerators i.e. for 7182,8574 is 6
LCM of denominators i.e. for 472,8000 is 472000.
Thus, GCF of Fractions is 6/472000.Finally, GCF of Fractions for 7182/472, 8574/8000 is 6/472000.