GCF of 8508/414, 4020/972
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8508/414, 4020/972 i.e 12/22356 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8508/414, 4020/972.
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 8508/414,4020/972?
Given fractions are 8508/414,4020/972
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 8508/414,4020/972, numerators are 8508,4020
Denominators are 414,972
The GCF of 8508,4020 is 12 .
LCM of 414,972 is 22356.
The greatest common factor of 8508/414,4020/972 = [GCF of 8508,4020]/[LCM of 414,972]= 12/22356
Therefore, the GCF of 8508/414,4020/972 is 12/22356.
To find the highest common factor of 8508,4020, we have to find the factors of both numbers and list the highest common factor.
The factors of 8508 are 1, 2, 3, 4, 6, 12, 709, 1418, 2127, 2836, 4254, 8508
The factors of 4020 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 67, 134, 201, 268, 335, 402, 670, 804, 1005, 1340, 2010, 4020
The HCF of 8508,4020 is 12.
Lets's calculate GCF of 8508,4020
| 2 | 8508, 4020 |
| 2 | 4254, 2010 |
| 3 | 2127, 1005 |
| 709, 335 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 8508,4020 By Matching Biggest Common Factor Method
Now, list down the factors of 8508
:1,2,3,4,6,12,709,1418,2127,2836,4254,8508
Now, list down the factors of 4020
:1,2,3,4,5,6,10,12,15,20,30,60,67,134,201,268,335,402,670,804,1005,1340,2010,4020
Greatest Common Factor
We found the factors 8508,4020 . The biggest common factor number is the GCF number.
So the greatest common factor 8508,4020 is 12.
Lets's calculate LCM of 414,972
| 2 | 414, 972 |
| 3 | 207, 486 |
| 3 | 69, 162 |
| 23, 54 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 23 x 54 = 22356
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/22356
Therefore, the GCF of Fractions 8508/414,4020/972 is 12/22356
Least Common Multiple of 414,972 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 414,972 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,972) = 18
common factors(in case of two or more numbers have common factors) = 1
GCF(414,972) x common factors =18 x 1 = 18
LCM(414,972) = ( 414 × 972 ) / 18
LCM(414,972) = 402408 / 18
LCM(414,972) = 22356
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FAQs on GCF of Fractions of 8508/414, 4020/972
1. What is the HCF of 8508,4020?
The HCF of 8508,4020 is 12
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 8508/414, 4020/972?
Answer: GCF of Numerators as per given numbers 8508/414, 4020/972 is
GCF of Numerators i.e. for 8508,4020 is 12
LCM of denominators i.e. for 414,972 is 22356.
Thus, GCF of Fractions is 12/22356.Finally, GCF of Fractions for 8508/414, 4020/972 is 12/22356.