GCF of 46/12, 208/45, 288/352
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 46/12, 208/45, 288/352 i.e 2/15840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 46/12, 208/45, 288/352.
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 46/12,208/45,288/352?
Given fractions are 46/12,208/45,288/352
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 46/12,208/45,288/352, numerators are 46,208,288
Denominators are 12,45,352
The GCF of 46,208,288 is 2 .
LCM of 12,45,352 is 15840.
The greatest common factor of 46/12,208/45,288/352 = [GCF of 46,208,288]/[LCM of 12,45,352]= 2/15840
Therefore, the GCF of 46/12,208/45,288/352 is 2/15840.
To find the highest common factor of 46,208,288, we have to find the factors of both numbers and list the highest common factor.
The factors of 46 are 1, 2, 23, 46
The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208
The factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
The HCF of 46,208,288 is 2.
Lets's calculate GCF of 46,208,288
| 2 | 46, 208, 288 |
| 23, 104, 144 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 46,208,288 By Matching Biggest Common Factor Method
Now, list down the factors of 46
:1,2,23,46
Now, list down the factors of 208
:1,2,4,8,13,16,26,52,104,208
Now, list down the factors of 288
:1,2,3,4,6,8,9,12,16,18,24,32,36,48,72,96,144,288
Greatest Common Factor
We found the factors 46,208,288 . The biggest common factor number is the GCF number.
So the greatest common factor 46,208,288 is 2.
Lets's calculate LCM of 12,45,352
| 2 | 12, 45, 352 |
| 2 | 6, 45, 176 |
| 3 | 3, 45, 88 |
| 1, 15, 88 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 1 x 15 x 88 = 15840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/15840
Therefore, the GCF of Fractions 46/12,208/45,288/352 is 2/15840
Least Common Multiple of 12,45,352 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 12,45,352 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,45,352) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(12,45,352) x common factors =1 x 12 = 12
LCM(12,45,352) = ( 12 × 45 × 352 ) / 12
LCM(12,45,352) = 190080 / 12
LCM(12,45,352) = 15840
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FAQs on GCF of Fractions of 46/12, 208/45, 288/352
1. What is the HCF of 46,208,288?
The HCF of 46,208,288 is 2
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 46/12, 208/45, 288/352?
Answer: GCF of Numerators as per given numbers 46/12, 208/45, 288/352 is
GCF of Numerators i.e. for 46,208,288 is 2
LCM of denominators i.e. for 12,45,352 is 15840.
Thus, GCF of Fractions is 2/15840.Finally, GCF of Fractions for 46/12, 208/45, 288/352 is 2/15840.