GCF of 869/92, 302/40, 116/75
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 869/92, 302/40, 116/75 i.e 1/13800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 869/92, 302/40, 116/75.
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 869/92,302/40,116/75?
Given fractions are 869/92,302/40,116/75
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 869/92,302/40,116/75, numerators are 869,302,116
Denominators are 92,40,75
The GCF of 869,302,116 is 1 .
LCM of 92,40,75 is 13800.
The greatest common factor of 869/92,302/40,116/75 = [GCF of 869,302,116]/[LCM of 92,40,75]= 1/13800
Therefore, the GCF of 869/92,302/40,116/75 is 1/13800.
To find the highest common factor of 869,302,116, we have to find the factors of both numbers and list the highest common factor.
The factors of 869 are 1, 11, 79, 869
The factors of 302 are 1, 2, 151, 302
The factors of 116 are 1, 2, 4, 29, 58, 116
The HCF of 869,302,116 is 1.
Lets's calculate GCF of 869,302,116
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 869,302,116 By Matching Biggest Common Factor Method
Now, list down the factors of 869
:1,11,79,869
Now, list down the factors of 302
:1,2,151,302
Now, list down the factors of 116
:1,2,4,29,58,116
Greatest Common Factor
We found the factors 869,302,116 . The biggest common factor number is the GCF number.
So the greatest common factor 869,302,116 is 1.
Lets's calculate LCM of 92,40,75
| 2 | 92, 40, 75 |
| 2 | 46, 20, 75 |
| 5 | 23, 10, 75 |
| 23, 2, 15 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 23 x 2 x 15 = 13800
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/13800
Therefore, the GCF of Fractions 869/92,302/40,116/75 is 1/13800
Least Common Multiple of 92,40,75 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 92,40,75 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(92,40,75) = 1
common factors(in case of two or more numbers have common factors) = 20
GCF(92,40,75) x common factors =1 x 20 = 20
LCM(92,40,75) = ( 92 × 40 × 75 ) / 20
LCM(92,40,75) = 276000 / 20
LCM(92,40,75) = 13800
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FAQs on GCF of Fractions of 869/92, 302/40, 116/75
1. What is the HCF of 869,302,116?
The HCF of 869,302,116 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 869/92, 302/40, 116/75?
Answer: GCF of Numerators as per given numbers 869/92, 302/40, 116/75 is
GCF of Numerators i.e. for 869,302,116 is 1
LCM of denominators i.e. for 92,40,75 is 13800.
Thus, GCF of Fractions is 1/13800.Finally, GCF of Fractions for 869/92, 302/40, 116/75 is 1/13800.