GCF of 48/912, 72/142, 684/544
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 48/912, 72/142, 684/544 i.e 12/2201568 easily. The following is the detailed procedure to determine the greatest common factor of fractions 48/912, 72/142, 684/544.
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 48/912,72/142,684/544?
Given fractions are 48/912,72/142,684/544
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 48/912,72/142,684/544, numerators are 48,72,684
Denominators are 912,142,544
The GCF of 48,72,684 is 12 .
LCM of 912,142,544 is 2201568.
The greatest common factor of 48/912,72/142,684/544 = [GCF of 48,72,684]/[LCM of 912,142,544]= 12/2201568
Therefore, the GCF of 48/912,72/142,684/544 is 12/2201568.
To find the highest common factor of 48,72,684, we have to find the factors of both numbers and list the highest common factor.
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The HCF of 48,72,684 is 12.
Lets's calculate GCF of 48,72,684
| 2 | 48, 72, 684 |
| 2 | 24, 36, 342 |
| 3 | 12, 18, 171 |
| 4, 6, 57 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 48,72,684 By Matching Biggest Common Factor Method
Now, list down the factors of 48
:1,2,3,4,6,8,12,16,24,48
Now, list down the factors of 72
:1,2,3,4,6,8,9,12,18,24,36,72
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Greatest Common Factor
We found the factors 48,72,684 . The biggest common factor number is the GCF number.
So the greatest common factor 48,72,684 is 12.
Lets's calculate LCM of 912,142,544
| 2 | 912, 142, 544 |
| 2 | 456, 71, 272 |
| 2 | 228, 71, 136 |
| 2 | 114, 71, 68 |
| 57, 71, 34 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 57 x 71 x 34 = 2201568
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/2201568
Therefore, the GCF of Fractions 48/912,72/142,684/544 is 12/2201568
Least Common Multiple of 912,142,544 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 912,142,544 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(912,142,544) = 2
common factors(in case of two or more numbers have common factors) = 16
GCF(912,142,544) x common factors =2 x 16 = 32
LCM(912,142,544) = ( 912 × 142 × 544 ) / 32
LCM(912,142,544) = 70450176 / 32
LCM(912,142,544) = 2201568
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 48/912, 72/142, 684/544
1. What is the HCF of 48,72,684?
The HCF of 48,72,684 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 48/912, 72/142, 684/544?
Answer: GCF of Numerators as per given numbers 48/912, 72/142, 684/544 is
GCF of Numerators i.e. for 48,72,684 is 12
LCM of denominators i.e. for 912,142,544 is 2201568.
Thus, GCF of Fractions is 12/2201568.Finally, GCF of Fractions for 48/912, 72/142, 684/544 is 12/2201568.