GCF of 144/69, 420/474
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 144/69, 420/474 i.e 12/10902 easily. The following is the detailed procedure to determine the greatest common factor of fractions 144/69, 420/474.
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 144/69,420/474?
Given fractions are 144/69,420/474
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 144/69,420/474, numerators are 144,420
Denominators are 69,474
The GCF of 144,420 is 12 .
LCM of 69,474 is 10902.
The greatest common factor of 144/69,420/474 = [GCF of 144,420]/[LCM of 69,474]= 12/10902
Therefore, the GCF of 144/69,420/474 is 12/10902.
To find the highest common factor of 144,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 144,420 is 12.
Lets's calculate GCF of 144,420
| 2 | 144, 420 |
| 2 | 72, 210 |
| 3 | 36, 105 |
| 12, 35 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 144,420 By Matching Biggest Common Factor Method
Now, list down the factors of 144
:1,2,3,4,6,8,9,12,16,18,24,36,48,72,144
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 144,420 . The biggest common factor number is the GCF number.
So the greatest common factor 144,420 is 12.
Lets's calculate LCM of 69,474
| 3 | 69, 474 |
| 23, 158 |
∴ So the LCM of the given numbers is 3 x 23 x 158 = 10902
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/10902
Therefore, the GCF of Fractions 144/69,420/474 is 12/10902
Least Common Multiple of 69,474 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 69,474 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(69,474) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(69,474) x common factors =3 x 1 = 3
LCM(69,474) = ( 69 × 474 ) / 3
LCM(69,474) = 32706 / 3
LCM(69,474) = 10902
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FAQs on GCF of Fractions of 144/69, 420/474
1. What is the HCF of 144,420?
The HCF of 144,420 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 144/69, 420/474?
Answer: GCF of Numerators as per given numbers 144/69, 420/474 is
GCF of Numerators i.e. for 144,420 is 12
LCM of denominators i.e. for 69,474 is 10902.
Thus, GCF of Fractions is 12/10902.Finally, GCF of Fractions for 144/69, 420/474 is 12/10902.