GCF of 7792/216, 8745/286
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7792/216, 8745/286 i.e 1/30888 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7792/216, 8745/286.
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 7792/216,8745/286?
Given fractions are 7792/216,8745/286
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 7792/216,8745/286, numerators are 7792,8745
Denominators are 216,286
The GCF of 7792,8745 is 1 .
LCM of 216,286 is 30888.
The greatest common factor of 7792/216,8745/286 = [GCF of 7792,8745]/[LCM of 216,286]= 1/30888
Therefore, the GCF of 7792/216,8745/286 is 1/30888.
To find the highest common factor of 7792,8745, we have to find the factors of both numbers and list the highest common factor.
The factors of 7792 are 1, 2, 4, 8, 16, 487, 974, 1948, 3896, 7792
The factors of 8745 are 1, 3, 5, 11, 15, 33, 53, 55, 159, 165, 265, 583, 795, 1749, 2915, 8745
The HCF of 7792,8745 is 1.
Lets's calculate GCF of 7792,8745
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 7792,8745 By Matching Biggest Common Factor Method
Now, list down the factors of 7792
:1,2,4,8,16,487,974,1948,3896,7792
Now, list down the factors of 8745
:1,3,5,11,15,33,53,55,159,165,265,583,795,1749,2915,8745
Greatest Common Factor
We found the factors 7792,8745 . The biggest common factor number is the GCF number.
So the greatest common factor 7792,8745 is 1.
Lets's calculate LCM of 216,286
| 2 | 216, 286 |
| 108, 143 |
∴ So the LCM of the given numbers is 2 x 108 x 143 = 30888
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/30888
Therefore, the GCF of Fractions 7792/216,8745/286 is 1/30888
Least Common Multiple of 216,286 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 216,286 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(216,286) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(216,286) x common factors =2 x 1 = 2
LCM(216,286) = ( 216 × 286 ) / 2
LCM(216,286) = 61776 / 2
LCM(216,286) = 30888
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FAQs on GCF of Fractions of 7792/216, 8745/286
1. What is the HCF of 7792,8745?
The HCF of 7792,8745 is 1
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 7792/216, 8745/286?
Answer: GCF of Numerators as per given numbers 7792/216, 8745/286 is
GCF of Numerators i.e. for 7792,8745 is 1
LCM of denominators i.e. for 216,286 is 30888.
Thus, GCF of Fractions is 1/30888.Finally, GCF of Fractions for 7792/216, 8745/286 is 1/30888.