GCF of 46/35, 76/21, 648/180
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 46/35, 76/21, 648/180 i.e 2/1260 easily. The following is the detailed procedure to determine the greatest common factor of fractions 46/35, 76/21, 648/180.
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 46/35,76/21,648/180?
Given fractions are 46/35,76/21,648/180
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 46/35,76/21,648/180, numerators are 46,76,648
Denominators are 35,21,180
The GCF of 46,76,648 is 2 .
LCM of 35,21,180 is 1260.
The greatest common factor of 46/35,76/21,648/180 = [GCF of 46,76,648]/[LCM of 35,21,180]= 2/1260
Therefore, the GCF of 46/35,76/21,648/180 is 2/1260.
To find the highest common factor of 46,76,648, 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 76 are 1, 2, 4, 19, 38, 76
The factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648
The HCF of 46,76,648 is 2.
Lets's calculate GCF of 46,76,648
| 2 | 46, 76, 648 |
| 23, 38, 324 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 46,76,648 By Matching Biggest Common Factor Method
Now, list down the factors of 46
:1,2,23,46
Now, list down the factors of 76
:1,2,4,19,38,76
Now, list down the factors of 648
:1,2,3,4,6,8,9,12,18,24,27,36,54,72,81,108,162,216,324,648
Greatest Common Factor
We found the factors 46,76,648 . The biggest common factor number is the GCF number.
So the greatest common factor 46,76,648 is 2.
Lets's calculate LCM of 35,21,180
| 3 | 35, 21, 180 |
| 5 | 35, 7, 60 |
| 7 | 7, 7, 12 |
| 1, 1, 12 |
∴ So the LCM of the given numbers is 3 x 5 x 7 x 1 x 1 x 12 = 1260
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1260
Therefore, the GCF of Fractions 46/35,76/21,648/180 is 2/1260
Least Common Multiple of 35,21,180 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 35,21,180 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(35,21,180) = 1
common factors(in case of two or more numbers have common factors) = 105
GCF(35,21,180) x common factors =1 x 105 = 105
LCM(35,21,180) = ( 35 × 21 × 180 ) / 105
LCM(35,21,180) = 132300 / 105
LCM(35,21,180) = 1260
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FAQs on GCF of Fractions of 46/35, 76/21, 648/180
1. What is the HCF of 46,76,648?
The HCF of 46,76,648 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 46/35, 76/21, 648/180?
Answer: GCF of Numerators as per given numbers 46/35, 76/21, 648/180 is
GCF of Numerators i.e. for 46,76,648 is 2
LCM of denominators i.e. for 35,21,180 is 1260.
Thus, GCF of Fractions is 2/1260.Finally, GCF of Fractions for 46/35, 76/21, 648/180 is 2/1260.