GCF of 42/306, 546/492, 115/868
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 42/306, 546/492, 115/868 i.e 1/5444964 easily. The following is the detailed procedure to determine the greatest common factor of fractions 42/306, 546/492, 115/868.
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 42/306,546/492,115/868?
Given fractions are 42/306,546/492,115/868
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 42/306,546/492,115/868, numerators are 42,546,115
Denominators are 306,492,868
The GCF of 42,546,115 is 1 .
LCM of 306,492,868 is 5444964.
The greatest common factor of 42/306,546/492,115/868 = [GCF of 42,546,115]/[LCM of 306,492,868]= 1/5444964
Therefore, the GCF of 42/306,546/492,115/868 is 1/5444964.
To find the highest common factor of 42,546,115, we have to find the factors of both numbers and list the highest common factor.
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
The factors of 115 are 1, 5, 23, 115
The HCF of 42,546,115 is 1.
Lets's calculate GCF of 42,546,115
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 42,546,115 By Matching Biggest Common Factor Method
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 546
:1,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546
Now, list down the factors of 115
:1,5,23,115
Greatest Common Factor
We found the factors 42,546,115 . The biggest common factor number is the GCF number.
So the greatest common factor 42,546,115 is 1.
Lets's calculate LCM of 306,492,868
| 2 | 306, 492, 868 |
| 2 | 153, 246, 434 |
| 3 | 153, 123, 217 |
| 51, 41, 217 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 51 x 41 x 217 = 5444964
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5444964
Therefore, the GCF of Fractions 42/306,546/492,115/868 is 1/5444964
Least Common Multiple of 306,492,868 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 306,492,868 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(306,492,868) = 2
common factors(in case of two or more numbers have common factors) = 12
GCF(306,492,868) x common factors =2 x 12 = 24
LCM(306,492,868) = ( 306 × 492 × 868 ) / 24
LCM(306,492,868) = 130679136 / 24
LCM(306,492,868) = 5444964
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FAQs on GCF of Fractions of 42/306, 546/492, 115/868
1. What is the HCF of 42,546,115?
The HCF of 42,546,115 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 42/306, 546/492, 115/868?
Answer: GCF of Numerators as per given numbers 42/306, 546/492, 115/868 is
GCF of Numerators i.e. for 42,546,115 is 1
LCM of denominators i.e. for 306,492,868 is 5444964.
Thus, GCF of Fractions is 1/5444964.Finally, GCF of Fractions for 42/306, 546/492, 115/868 is 1/5444964.