GCF of 180/42, 288/90, 169/105
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 180/42, 288/90, 169/105 i.e 1/630 easily. The following is the detailed procedure to determine the greatest common factor of fractions 180/42, 288/90, 169/105.
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 180/42,288/90,169/105?
Given fractions are 180/42,288/90,169/105
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 180/42,288/90,169/105, numerators are 180,288,169
Denominators are 42,90,105
The GCF of 180,288,169 is 1 .
LCM of 42,90,105 is 630.
The greatest common factor of 180/42,288/90,169/105 = [GCF of 180,288,169]/[LCM of 42,90,105]= 1/630
Therefore, the GCF of 180/42,288/90,169/105 is 1/630.
To find the highest common factor of 180,288,169, we have to find the factors of both numbers and list the highest common factor.
The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
The factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
The factors of 169 are 1, 13, 169
The HCF of 180,288,169 is 1.
Lets's calculate GCF of 180,288,169
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 180,288,169 By Matching Biggest Common Factor Method
Now, list down the factors of 180
:1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180
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
Now, list down the factors of 169
:1,13,169
Greatest Common Factor
We found the factors 180,288,169 . The biggest common factor number is the GCF number.
So the greatest common factor 180,288,169 is 1.
Lets's calculate LCM of 42,90,105
| 2 | 42, 90, 105 |
| 3 | 21, 45, 105 |
| 5 | 7, 15, 35 |
| 7 | 7, 3, 7 |
| 1, 3, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 7 x 1 x 3 x 1 = 630
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/630
Therefore, the GCF of Fractions 180/42,288/90,169/105 is 1/630
Least Common Multiple of 42,90,105 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 42,90,105 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,90,105) = 3
common factors(in case of two or more numbers have common factors) = 210
GCF(42,90,105) x common factors =3 x 210 = 630
LCM(42,90,105) = ( 42 × 90 × 105 ) / 630
LCM(42,90,105) = 396900 / 630
LCM(42,90,105) = 630
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FAQs on GCF of Fractions of 180/42, 288/90, 169/105
1. What is the HCF of 180,288,169?
The HCF of 180,288,169 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 180/42, 288/90, 169/105?
Answer: GCF of Numerators as per given numbers 180/42, 288/90, 169/105 is
GCF of Numerators i.e. for 180,288,169 is 1
LCM of denominators i.e. for 42,90,105 is 630.
Thus, GCF of Fractions is 1/630.Finally, GCF of Fractions for 180/42, 288/90, 169/105 is 1/630.